M. Santana | Searcharxiv

arXiv2019

Visible Analysis of NASA Lucy Mission Targets Eurybates, Polymele, Orus and Donaldjohanson

Jupiter Trojan asteroids are minor bodies that share Jupiter's orbit around the Sun. Although not yet well understood in origin and composition, they have surface properties that, besides being comparable with other populations of small bodies in the Solar System, hold information that may restrict models of planetary formation. Due their importance, there has been a significant increase in an interest in studying this population. In this context arises the NASA Lucy Mission, with a planned launch of 2021. The Lucy Mission will be the first one to address a group of 6 objects with the aim of investigating, in detail, their nature. In order to provide valuable information for mission planning and maximize the scientific return, we carried out ground based observations of four targets of the mission. Aimed at looking for variabilities on the spectra of (3548) Eurybates, (15094) Polymele and (21900) Orus, we performed rotationally resolved visible spectroscopy of them at SOAR Telescope. We also analyzed the first visible spectrum obtained for the main belt asteroid (52246) Donaldjohanson at Gran Telescopio Canarias. The spectra of Orus and Polymele present rather homogeneous characteristics along the surfaces, and their taxa correspond with those of the two dominant populations in the Trojan population, the P- and the D-type group of objects. Spectroscopy of Eurybates, on the other side, suggests that some variation on the characteristics of the reflectance of this body could be related with its collisional history. Donaldjohanson, the only main belt object in the group of targets, shows, according to our visible spectrum, hints of the presence of hydrated materials. Lucy mission will investigate the surface composition of these targets and will shed light on their connections with other minor bodies populations and in their role on the evolution of the Solar System.

astro-ph.EP↗

arXiv2015

Landau's Theorem Revisited Again

We give a new proof of the sufficiency of Landau's conditions for a non-decreasing sequence of integers to be the score sequence of a tournament. The proof involves jumping down a total order on sequences satisfying Landau's conditions and provides a $O(n^2)$ algorithm that can be used to construct a tournament whose score sequence is any in the total order. We also compare this algorithm with to other algorithms that jump along this total order, one jumping down and one jumping up.

math.CO↗

arXiv2015

Strong chromatic index of subcubic planar multigraphs

The strong chromatic index of a multigraph is the minimum $k$ such that the edge set can be $k$-colored requiring that each color class induces a matching. We verify a conjecture of Faudree, Gyárfás, Schelp and Tuza, showing that every planar multigraph with maximum degree at most 3 has strong chromatic index at most 9, which is sharp.

math.CO↗

arXiv2015

$k$-intersection edge-coloring subcubic planar multigraphs

Given an edge-coloring of a simple graph, assign to every vertex $v$ a set $S_v$ comprised of the colors used on the edges incident to $v$. The $k$-intersection chromatic index of a graph is the minimum $t$ such that the edge set can be properly $t$-colored, additionally requiring that for every two adjacent vertices $u$ and $v$, $|S_u \cap S_v| \le k$. For all $k \neq 2$, this value is known for subcubic planar graphs, and furthermore, these values are best possible. We naturally extend this definition to multigraphs with bounded edge multiplicity, and we show that every subcubic planar multigraph with edge multiplicity at most two has 2-intersection chromatic index at most 5, which is sharp.

math.CO↗