arXiv subjects

P. Francis

Publications and source records attributed to P. Francis.

16 recordsLinked to original sources

arXiv2026

AT2025agpz in Rubin commissioning data: distinguishing a luminous interacting supernova from nuclear transients in compact galaxies

The Vera C. Rubin Observatory's Legacy Survey of Space and Time will discover unprecedented numbers of rare, long-lived optical transients, many of which will be too faint or too numerous for comprehensive spectroscopic follow-up. Characterising objects that span the boundaries between established transient classes is therefore essential for improving photometric classification. We present AT2025agpz, a luminous transient at $z=0.147$, discovered around peak by ATLAS but extensively monitored during Rubin commissioning observations of the Euclid Deep Field South. The transient is coincident with the nucleus of a faint dwarf galaxy, exhibits a rest-frame rise time of $77.9\pm1.3$ d, and reaches a peak bolometric luminosity of $6.3\times10^{43}$ erg s$^{-1}$. The exceptional depth and cadence of the Rubin commissioning data, combined with complementary DECam imaging, tightly constrain the explosion epoch and yield an early-time power-law rise of $n=3.33^{+0.33}_{-0.28}$. Follow-up spectroscopy reveals remarkably slow spectral evolution dominated by narrow Balmer emission, while high-resolution X-shooter observations resolve broad electron-scattering wings and multiple H$\alpha$ emission components characteristic of interaction-powered supernovae. Spectral energy distribution modelling indicates a low-mass, moderately star-forming host galaxy. Although AT2025agpz occupies observational parameter space shared by the recently identified Ambiguous Nuclear Transient population, its colour evolution, host environment, and emission-line morphology favour an interaction-powered luminous supernova. More broadly, this event highlights the growing observational overlap between luminous interacting supernovae and nuclear transients, illustrating both the challenges and opportunities for transient classification in the Rubin era.

astro-ph.HE↗

arXiv2024

Maximal Independent Sets in Planar Triangulations

We show that every planar triangulation on $n$ vertices has a maximal independent set of size at most $n/3$. This affirms a conjecture by Botler, Fernandes and Guti\'errez [Electron.\ J.\ Comb., 2024], which in turn would follow if an open question of Goddard and Henning [Appl.\ Math.\ Comput., 2020] which asks if every planar triangulation has three disjoint maximal independent sets were answered in the affirmative. Since a maximal independent set is a special type of dominating set (independent dominating set), this is a structural strengthening of a major result by Matheson and Tarjan [Eur.\ J.\ Comb., 1996] that every triangulated disc has a dominating set of size at most $n/3$, but restricted to triangulations.

math.CO↗

arXiv2024

Face-hitting Dominating Sets in Planar Graphs

A dominating set of a graph $G$ is a subset $S$ of its vertices such that each vertex of $G$ not in $S$ has a neighbor in $S$. A face-hitting set of a plane graph $G$ is a set $T$ of vertices in $G$ such that every face of $G$ contains at least one vertex of $T$. We show that the vertex-set of every plane (multi-)graph without isolated vertices, self-loops or $2$-faces can be partitioned into two disjoint sets so that both the sets are dominating and face-hitting. We also show that all the three assumptions above are necessary for the conclusion. As a corollary, we show that every $n$-vertex simple plane triangulation has a dominating set of size at most $(1 - \alpha)n/2$, where $\alpha n$ is the maximum size of an independent set in the triangulation. Matheson and Tarjan [European J. Combin., 1996] conjectured that every plane triangulation with a sufficiently large number of vertices $n$ has a dominating set of size at most $n / 4$. Currently, the best known general bound for this is by Christiansen, Rotenberg and Rutschmann [SODA, 2024] who showed that every plane triangulation on $n > 10$ vertices has a dominating set of size at most $2n/7$. Our corollary improves their bound for $n$-vertex plane triangulations which contain a maximal independent set of size either less than $2n/7$ or more than $3n/7$.

math.CO↗

arXiv2022

Disjoint Total Dominating Sets in Near-Triangulations

We show that every simple planar near-triangulation with minimum degree at least three contains two disjoint total dominating sets. The class includes all simple planar triangulations other than the triangle. This affirms a conjecture of Goddard and Henning [Thoroughly dispersed colorings, J. Graph Theory, 88 (2018) 174-191].

math.CO↗

arXiv2022

$χ$-binding functions for some classes of $(P_3\cup P_2)$-free graphs

The class of $2K_2$-free graphs have been well studied in various contexts in the past. It is known that the class of $\{2K_2,2K_1+K_p\}$-free graphs and $\{2K_2,(K_1\cup K_2)+K_p\}$-free graphs admits a linear $χ$-binding function. In this paper, we study the classes of $(P_3\cup P_2)$-free graphs which is a superclass of $2K_2$-free graphs. We show that $\{P_3\cup P_2,2K_1+K_p\}$-free graphs and $\{P_3\cup P_2,(K_1\cup K_2)+K_p\}$-free graphs also admits linear $χ$-binding functions. In addition, we give tight chromatic bounds for $\{P_3\cup P_2,HVN\}$-free graphs and $\{P_3\cup P_2,diamond\}$-free graphs and it can be seen that the latter is an improvement of the existing bound given by A. P. Bharathi and S. A. Choudum [Colouring of $(P_3\cup P_2)$-free graphs, Graphs and Combinatorics 34 (2018), 97-107].

math.CO↗

arXiv2021

On Domatic and Total Domatic Numbers of Product Graphs

A \emph{domatic} (\emph{total domatic}) \emph{$k$-coloring} of a graph $G$ is an assignment of $k$ colors to the vertices of $G$ such that each vertex contains vertices of all $k$ colors in its closed neighborhood (neighborhood). The \emph{domatic} (\emph{total domatic}) \emph{number} of $G$, denoted $d(G)$ ($d_t (G)$), is the maximum $k$ for which $G$ has a domatic (total domatic) $k$-coloring. In this paper, we show that for two non-trivial graphs $G$ and $H$, the domatic and total domatic numbers of their Cartesian product $G \cart H$ is bounded above by $\max\{|V(G)|, |V(H)|\}$ and below by $\max\{d(G), d(H)\}$. Both these bounds are tight for an infinite family of graphs. Further, we show that if $H$ is bipartite, then $d_t(G \cart H)$ is bounded below by $2\min\{d_t(G),d_t(H)\}$ and $d(G \cart H)$ is bounded below by $2\min\{d(G),d_t(H)\}$. These bounds give easy proofs for many of the known bounds on the domatic and total domatic numbers of hypercubes \cite{chen,zel4} and the domination and total domination numbers of hypercubes \cite{har,joh} and also give new bounds for Hamming graphs. We also obtain the domatic (total domatic) number and domination (total domination) number of $n$-dimensional torus $\mathop{\cart}\limits_{i=1}^{n} C_{k_i}$ with some suitable conditions to each $k_i$, which turns out to be a generalization of a result due to Gravier \cite{grav2} %[\emph{Total domination number of grid graphs}, Discrete Appl. Math. 121 (2002) 119-128] and give easy proof of a result due to Klavžar and Seifter \cite{sand}.

math.CO↗

arXiv2021

Bounds for the b-chromatic number of powers of hypercubes

The b-chromatic number $b(G)$ of a graph $G$ is the maximum $k$ for which $G$ has a proper vertex coloring using $k$ colors such that each color class contains at least one vertex adjacent to a vertex of every other color class. In this paper, we mainly investigate on one of the open problems given in [P. Francis, S. Francis Raj, On b-coloring of powers of hypercubes, Discrete Appl. Math. 225 (2017) 74-86.]. As a consequence, we have obtained an upper bound for the b-chromatic number of some powers of hypercubes. This turns out to be an improvement of the already existing bound in [P. Francis, S. Francis Raj, On b-coloring of powers of hypercubes, Discrete Appl. Math. 225 (2017) 74-86.]. Further, we have determined a lower bound for the b-chromatic number of some powers of the Hamming graph, a generalization of the hypercube.

math.CO↗

arXiv2020

On indicated coloring of lexicographic product of graphs

Indicated coloring is a graph coloring game in which two players collectively color the vertices of a graph in the following way. In each round the first player (Ann) selects a vertex, and then the second player (Ben) colors it properly, using a fixed set of colors. The goal of Ann is to achieve a proper coloring of the whole graph, while Ben is trying to prevent the realization of this project. The smallest number of colors necessary for Ann to win the game on a graph $G$ (regardless of Ben's strategy) is called the indicated chromatic number of $G$, denoted by $χ_i(G)$. In this paper, we have shown that for any graphs $G$ and $H$, $G[H]$ is $k$-indicated colorable for all $k\geq\mathrm{col}(G)\mathrm{col}(H)$. Also, we have shown that for any graph $G$ and for some classes of graphs $H$ with $χ(H)=χ_i(H)=\ell$, $G[H]$ is $k$-indicated colorable if and only if $G[K_\ell]$ is $k$-indicated colorable. As a consequence of this result we have shown that for some particular families of graphs $G$ and $H$, $G[H]$ is $k$-indicated colorable for every $k\geq χ(G[H])$. This serves as a partial answer to one of the questions raised by A. Grzesik in \cite{and}. In addition, if $G$ is a Bipartite graph or a $\{P_5,K_3\}$-free graph (or) a $\{P_5,Paw\}$-free graph and if $H$ is from the same families of graphs, then we have shown that $χ_i(G[H])=χ(G[H])$.

math.CO↗

arXiv2018

On indicated coloring of some classes of graphs

Indicated coloring is a type of game coloring in which two players collectively color the vertices of a graph in the following way. In each round the first player (Ann) selects a vertex, and then the second player (Ben) colors it properly, using a fixed set of colors. The goal of Ann is to achieve a proper coloring of the whole graph, while Ben is trying to prevent the realization of this project. The smallest number of colors necessary for Ann to win the game on a graph $G$ (regardless of Ben's strategy) is called the indicated chromatic number of $G$, denoted by $χ_i(G)$. In this paper, we obtain structural characterization of connected $\{P_5,K_4,Kite,Bull\}$-free graphs which contains an induced $C_5$ and connected $\{P_6,C_5, K_{1,3}\}$-free graphs that contains an induced $C_6$. Also, we prove that $\{P_5,K_4,Kite,Bull\}$-free graphs that contains an induced $C_5$ and $\{P_6,C_5,\overline{P_5}, K_{1,3}\}$-free graphs which contains an induced $C_6$ are $k$-indicated colorable for all $k\geqχ(G)$. In addition, we show that $\mathbb{K}[C_5]$ is $k$-indicated colorable for all $k\geqχ(G)$ and as a consequence, we exhibit that $\{P_2\cup P_3, C_4\}$-free graphs, $\{P_5,C_4\}$-free graphs are $k$-indicated colorable for all $k\geqχ(G)$. This partially answers one of the questions which was raised by A. Grzesik in \cite{and}.

math.CO↗

arXiv2015

What Powers Lyman alpha Blobs?

Lyman alpha blobs (LABs) are spatially extended lyman alpha nebulae seen at high redshift. The origin of Lyman alpha emission in the LABs is still unclear and under debate. To study their heating mechanism(s), we present Australia Telescope Compact Array (ATCA) observations of the 20 cm radio emission and Herschel PACS and SPIRE measurements of the far-infrared (FIR) emission towards the four LABs in the protocluster J2143-4423 at z=2.38. Among the four LABs, B6 and B7 are detected in the radio with fluxes of 67+/-17 microJy and 77+/-16 microJy, respectively, and B5 is marginally detected at 3 sigma (51+/-16 microJy). For all detected sources, their radio positions are consistent with the central positions of the LABs. B6 and B7 are obviously also detected in the FIR. By fitting the data with different templates, we obtained redshifts of 2.20$^{+0.30}_{-0.35}$ for B6 and 2.20$^{+0.45}_{-0.30}$ for B7 which are consistent with the redshift of the lyman alpha emission within uncertainties, indicating that both FIR sources are likely associated with the LABs. The associated FIR emission in B6 and B7 and high star formation rates strongly favor star formation in galaxies as an important powering source for the lyman alpha emission in both LABs. However, the other two, B1 and B5, are predominantly driven by the active galactic nuclei or other sources of energy still to be specified, but not mainly by star formation. In general, the LABs are powered by quite diverse sources of energy.

astro-ph.GA↗

arXiv2012

2008 LC18: a potentially unstable Neptune Trojan

The recent discovery of the first Neptune Trojan at the planet's trailing (L5) Lagrange point, 2008 LC18, offers an opportunity to confirm the formation mechanism of a member of this important tracer population for the Solar system's dynamical history. We tested the stability of 2008 LC18's orbit through a detailed dynamical study, using test particles spread across the orbital uncertainties in a, e, i and Ω. This showed that the wide uncertainties of the published orbit span regions of both extreme dynamical instability, with lifetimes < 100 Myr, and with significant stability (> 1 Gyr lifetimes). The stability of 2008 LC18's clones is greatly dependent on their semi-major axis and only weakly correlated with their eccentricity. Test particles on orbits with an initial semi-major axis less than 29.91 AU have dynamical half-lives shorter than 100 Myr; in contrast, particles with an initial semi-major axis greater than 29.91 AU exhibit such strong dynamical stability that almost all are retained over the 1 Gyr of our simulations. More observations of this object are necessary to improve the orbit. If 2008 LC18 is in the unstable region, then our simulations imply that it is either a temporary Trojan capture, or a representative of a slowly decaying Trojan population (like its sibling the L4 Neptunian Trojan 2001 QR322), and that it may not be primordial. Alternatively, if the orbit falls into the larger, stable region, then 2008 LC18 is a primordial member of the highly stable and highly inclined component of the Neptune Trojan population, joining 2005 TN53 and 2007 VL305. We attempted to recover 2008 LC18 using the 2.3m telescope at Siding Spring Observatory to provide this astrometry, but were unsuccessful due to the high stellar density of its current sky location near the galactic centre. The recovery of this object will require a telescope in the 8m class.

astro-ph.EP↗

arXiv2011

On the absence of molecular absorption in high redshift millimetre-band searches

We have undertaken a search for millimetre-wave band absorption (through the CO and HCO+ rotational transitions) in the host galaxies of reddened radio sources (z = 0.405-1.802). Despite the colour selection (optical-near infrared colours of V - K > 5 in all but one source), no absorption was found in any of the eight quasars for which the background continuum flux was detected. On the basis of the previous (mostly intervening) H2 and OH detections, the limits reached here and in some previous surveys should be deep enough to detect molecular absorption according to their V - K colours. However, our survey makes the assumption that the reddening is associated with dust close to the emission redshift of the quasar and that the narrow millimetre component of this emission is intercepted by the compact molecular cores. By using the known millimetre absorbers to define the colour depth and comparing this with the ultra-violet luminosities of the sources, we find that, even if these assumptions are valid, only twelve of the forty objects (mainly from this work) are potentially detectable. This is assuming an excitation temperature of 10 K at z=0, with the number decreasing with increasing temperatures (to zero detectable at 100 K).

astro-ph.CO↗

arXiv2010

Redshifted HI and OH absorption in radio galaxies and quasars

From a survey for redshifted HI 21-cm and OH 18-cm absorption in the hosts of a sample of radio galaxies and quasars, we detect HI in three of the ten and OH in none of the fourteen sources for which useful data were obtained. As expected from our recent result, all of the 21-cm detections occur in sources with ultra-violet continuum luminosities of L < 10^23 W/Hz. At these "moderate" luminosities, we also obtain four non-detections, although, as confirmed by the equipartition of detections between the type-1 and type-2 objects, this near-50% detection rate cannot be attributed to unified schemes of active galactic nuclei (AGN). All of our detections are at redshifts of z < 0.67, which, in conjunction with our faint source selection, biases against UV luminous objects. The importance of ultra-violet luminosity (over AGN type) in the detection of 21-cm is further supported by the non-detections in the two high redshift z ~ 3.6 - 3.8 radio galaxies, which are both type-2 objects, while having L > 10^23 W/Hz. Our 21-cm detections in combination with those previously published, give a total of eight (associated and intervening) HI absorbing sources searched and undetected in OH. Using the detected 21-cm line strengths to normalise the limits, we find that only two of these eight may have been searched sufficiently deeply in OH, although even these are marginal.

astro-ph.CO↗

arXiv2009

HeII emission in Lyman-alpha nebulae: AGN or cooling radiation?

We present a study of an extended Lyman-alpha (Lya) nebula located in a known overdensity at z~2.38. The data include multiwavelength photometry covering the rest-frame spectral range from 0.1 to 250um, and deep optical spectra of the sources associated with the extended emission. Two galaxies are associated with the Lya nebula. One of them is a dust enshrouded AGN, while the other is a powerful starburst, forming stars at >~600 Msol/yr. We detect the HeII emission line at 1640A in the spectrum of the obscured AGN, but detect no emission from other highly ionized metals (CIV or NV) as is expected from an AGN. One scenario that simultaneously reproduces the width of the detected emission lines, the lack of CIV emission, and the geometry of the emitting gas, is that the HeII and the Lya emission are the result of cooling gas that is being accreted on the dark matter halo of the two galaxies, Ly1 and Ly2. Given the complexity of the environment associated with our Lya nebula it is possible that various mechanisms of excitation are at work simultaneously.

astro-ph.CO↗

arXiv2009

The effect of dust geometry on the Lyman-alpha output of galaxies

We present the optical spectroscopic follow-up of 31 z=0.3 Lyman-alpha (Lya) emitters, previously identified by Deharveng et al. (2008). We find that 17% of the Lya emitters have line ratios that require the hard ionizing continuum produced by an AGN. The uniform dust screen geometry traditionally used in studies similar to ours is not able to simultaneously reproduce the observed high Lya/Halpha and Halpha/Hbeta line ratios. We consider different possibilities for the geometry of the dust around the emitting sources. We find that also a uniform mixture of sources and dust does not reproduce the observed line ratios. Instead, these are well reproduced by a clumpy dust screen. This more realistic treatment of the geometry results in extinction corrected (Lya/Halpha)_C values consistent with Case B recombination theory, whereas a uniform dust screen model would imply values (Lya/Halpha)_C higher than 8.7. Our analysis shows that there is no need to invoke "ad-hoc" multi phase media in which the Lya photons only scatter between the dusty clouds and eventually escape.

astro-ph.CO↗

arXiv2007

SkyMapper and the Southern Sky Survey

This paper presents the design and science goals for the SkyMapper telescope. SkyMapper is a 1.3m telescope featuring a 5.7 square degree field-of-view Cassegrain imager commissioned for the Australian National University's Research School of Astronomy and Astrophysics. It is located at Siding Spring Observatory, Coonabarabran, NSW, Australia and will see first light in late 2007. The imager possesses 16kx16k 0.5 arcsec pixels. The primary scientific goal of the facility is to perform the Southern Sky Survey, a six colour and multi-epoch (4 hour, 1 day, 1 week, 1 month, 1 year sampling) photometric survey of the southerly 2pi steradians to g~23 mag. The survey will provide photometry to better than 3% global accuracy and astrometry to better than 50 mas. Data will be supplied to the community as part of the Virtual Observatory effort. The survey will take five years to complete.

astro-ph↗