arXiv subjects

Jin Yan

Publications and source records attributed to Jin Yan.

At least 19 recordsLinked to original sources

arXiv2026

Interior Curvature Estimates for the Graphical Scalar Curvature Equation in All Dimensions

We resolve the long-standing problem of establishing interior $C^2$ estimates for admissible solutions of the graphical scalar curvature equation in every dimension $n\ge 3$. More precisely, we prove interior curvature estimates for admissible solutions to the constant graphical scalar curvature equation. The proof combines Jacobi inequalities with a two-surface maximum principle and a two-surface Pogorelov estimate.

math.AP↗

arXiv2026

The asymptotic Plateau problem for Hypersurfaces of constant $H_{k}$ curvature in hyperbolic space

In this paper, we study the asymptotic Plateau problem in hyperbolic space for hypersurfaces of constant $H_k$-curvature. We prove the existence of a smooth complete $k$-convex hypersurface in $\mathbb{H}^{n+1}$ satisfying \[ H_k(\kappa)=\sigma, \qquad \sigma\in(0,1), \] with prescribed asymptotic boundary at infinity. In particular, our result extends the range of the constant $\sigma$ in the existence theorem of Guan and Spruck [J. Eur. Math. Soc. 12 (2010), no. 3, 797--817] for $H_{k}$ curvature to the full interval $(0,1)$.

math.DG↗

arXiv2026

A Chv\'atal--Erd\H{o}s type condition for supereulerian digraphs with $\alpha_{2}=4$

A digraph is \textbf{supereulerian} if it contains a spanning closed trail. Let $\alpha_2(D)$ denote the maximum cardinality of a vertex set inducing no 2-cycle. In this paper, we characterize supereulerianity in a strong digraph $D$ with $\alpha_2(D)=4$ by proving that a strong digraph $D$ with $\alpha_2(D)=4$ and $\lambda(D)\ge 2$ is supereulerian if and only if $D$ does not belong to an exceptional family $\mathcal H$ of $2$-arc-strong digraphs with $\alpha_2(D)=4$. Furthermore, every strong digraph satisfying $\alpha_2(D)=4$ and $\lambda(D)\geq3$ is supereulerian.

math.CO↗

arXiv2026

Packing and Covering Cycles Through Prescribed Vertices

Let $G$ be a finite simple graph and let $S\subseteq V(G)$. We prove that the minimum number of vertices meeting every cycle that intersects $S$ is at most the maximum number of vertices of $S$ covered by a collection of vertex-disjoint cycles. This answers a question posed by Bowler, Ghorbani, Gut, Jacobs, and Reich [\emph{SIAM Journal on Discrete Mathematics} \textbf{40} (2026), 988--999]. An incidence-based reduction to their bidirected packing--covering theorem preserves the packing value and projects transversals without increasing their cardinality.

math.CO↗

arXiv2026

Global Curvature Estimates for $\sigma_k$ Curvature Equations with $k\geq n/2$

We establish a new concavity inequality for the elementary symmetric function $\sigma_k$, which controls the spectral quadratic form arising from the second variation of $\log\lambda_{\max}$. The proof is based on an easy--hard decomposition of the spectral variables. The easy region is treated using an optimal constrained concavity estimate for $\sigma_k$, whereas the hard region is analyzed through G{\aa}rding-root coordinates and the concavity of the ordered partial sums of the inverse roots. As an application, for $n/2\leq k<n$, we obtain global curvature estimates for closed star-shaped $k$-convex hypersurfaces satisfying $\sigma_k(\kappa)=f(X,\nu)$ with a general positive right-hand side, together with the corresponding global-to-boundary estimates for Euclidean Hessian equations.

math.AP↗

arXiv2026

Complexity of Arc-Decompositions involving Perfect Matchings and Cycle Factors

For two digraph properties $P_1$ and $P_2$, a $(P_1,P_2)$-arc-decomposition of a digraph $D$ is a partition $A(D)=A_1\mathbin{\dot\cup}A_2$ such that the spanning subdigraphs $D[A_1]$ and $D[A_2]$ have properties $P_1$ and $P_2$, respectively. For example, a (strong,strong)-arc-decomposition of a digraph $D=(V,A)$ is a partitioning $A=A_1\cup{}A_2$ of $A$ so that each of the spanning digraphs $D_i=(V,A_i)$, $i=1,2$ are strongly connected. We prove that it is NP-complete to decide whether a digraph admits an arc-decomposition with properties $(P_1,P_2)$ where $(P_1,P_2)\in \{$(is a perfect matching, having no odd directed cycle), (perfect matching, strong), (perfect matching, having an out-branching), (is a cycle factor, having no odd directed cycle)$\}$. These results settle some open problems posed by Bang-Jensen, Bessy, Gon\c{c}alves, and Picasarri-Arrieta [Theoret. Comput. Sci. 928 (2022), 167--182].

math.CO↗

arXiv2026

Efficient production of $^{229m,g}$Th via neutron capture in VUV-transparent crystals

The low-lying isomeric state of $^{229m}$Th, owing to its unique nuclear energy structure, has been widely regarded as one of the most promising candidates for the development of a nuclear clock. However, the limited availability of suitable $^{229}$Th sources with sufficiently high activity remains a major challenge for experimental investigations of the $^{229m}$Th isomer. We propose a neutron-capture-based approach for the in-situ production of $^{229m,g}$Th by doping $^{228}$Ra into crystal hosts, where $^{229m,g}$Th is generated through neutron-capture reactions followed by a sequence of radioactive decay processes. We systematically investigate the background contributions associated with the three doped crystal hosts, namely CaF$_2$, SrF$_2$, and LiF, and evaluate their impact on the detection and identification of $^{229m}$Th. Under a neutron flux of $10^{15}\ \mathrm{n/cm^{2}/s}$ and a $^{228}$Ra doping concentration of $10^{19}\ \mathrm{cm^{-3}}$, the proposed method is capable of producing on the order of $10^{12}$ $^{229}$Th and $^{229m}$Th nuclei within only 1 s of irradiation, with a signal-to-noise ratios as high as $10^5$. In addition, the influences of detector wavelength resolution and post-irradiation measurement time on the detectability of the $^{229m}$Th signal are systematically analyzed, and the corresponding optimal measurement conditions are identified. Furthermore, the spatial distribution of neutron-produced $^{229}$Th within the crystal is investigated, providing practical guidance for optimizing crystal geometry and illumination configuration in future continuous-wave VUV absorption spectroscopy experiments. These results suggest that the proposed scheme provides a promising alternative pathway for the production and detection of $^{229\mathrm{m,g}}$Th, which may facilitate future studies toward the realization of nuclear-clock-based technologies.

nucl-ex↗

arXiv2026

Hitting Maximum Independent Sets in Dense and Highly Connected Graphs

For a graph $G$, let $h(G)$ be the minimum cardinality of a vertex set meeting every maximum independent set of $G$. We establish two complementary reduction principles for the Bollob\'as--Erd\H{o}s--Tuza conjecture: the conjecture for arbitrary graphs is equivalent to its restriction to regular graphs of any fixed positive linear degree, and, within every hereditary graph class, a uniform sublinear bound is equivalent to a sublinear bound on graphs of every fixed positive linear vertex connectivity. We prove the sharp general estimate \[ h(G)\le \left\lfloor\frac{|V(G)|}{2\alpha(G)+\delta(G)-|V(G)|}\right\rfloor \] whenever the denominator is positive, with equality for balanced complete multipartite graphs. Consequently, every $3$-colorable graph of order $n$ with $\kappa(G)\ge\rho n$ and $\rho>1/3$ has a hitting set of size at most $\lfloor(\rho-1/3)^{-1}\rfloor$; direct use of a $3$-coloring improves this to $6$ when $\kappa(G)>4n/9$ and to the sharp bound $3$ when $\kappa(G)>n/2$. For dense regular graphs with independence ratio greater than $1/4$, we obtain a logarithmic bound, while constructions with linear degree and linear independence number show that $h(G)=\Omega(\sqrt n)$ can still occur. We also prove a logarithmic bound for near-regular $3$-colorable graphs and exhibit a critical family at connectivity $n/3$ that explains the limitations of the degree-surplus and degree-ratio methods.

math.CO↗

arXiv2026

Paths with Prescribed Endpoints in Semicomplete and Locally Semicomplete Digraphs

We study two open path problems with prescribed endpoints posed by Bang-Jensen and Gutin. The first asks for a longest $(x,y)$-path in a semicomplete digraph. The second asks whether a locally semicomplete digraph has a Hamiltonian $(x,y)$-path. For semicomplete digraphs, we solve the first problem when the endpoints lie in different strong components. We also prove that if a non-Hamiltonian longest $(x,y)$-path omits a set of vertices, then these vertices together with $x$ and $y$ have a Hamiltonian $(y,x)$-path. This gives an equivalent cycle problem. We then give an exact algorithm that runs in polynomial time when the number of omitted vertices is fixed. For locally semicomplete digraphs, we determine the possible endpoints in the connected nonstrong case. Known results then leave only strong, nonsemicomplete, non-$4$-strong digraphs unresolved. Every such digraph of order at least five has a strong vertex cut of size at most three. Two examples show that a spanning directed path together with a vertex-disjoint directed cycle is not sufficient, and that vertices of one strong component need not occur consecutively on a Hamiltonian path.

math.CO↗

arXiv2026

Spanning $H$-subdivisions with Prescribed Path Lengths

We study spanning $H$-subdivisions in dense graphs where the length of every subdivision path is prescribed in advance. This problem is motivated in part by a question of Pavez-Sign\'e [Combin. Probab. Comput. 33 (2024), 121--128], who asked whether the subdivision paths in a spanning $H$-subdivision can be required to have similar lengths. Let $h\ge3$ be an integer and let $0<\beta\ll\alpha\ll1/h$. We prove that, for all sufficiently large $n$, every $n$-vertex graph $G$ with $\delta(G)\ge n/2+\lfloor h/3\rfloor$ has the following property. For every graph $H$ with $h$ edges and no isolated vertices, write $E(H)=\{e_1,\ldots,e_h\}$, and every choice of integers $\ell_1,\ldots,\ell_h\ge4$ satisfying $\sum_{i=1}^h\ell_i=n-|V(H)|+h$ and $\sum_{\ell_i<\alpha n}\ell_i\le\beta n$, the graph $G$ contains a spanning $H$-subdivision in which the $i$th edge of $H$ is replaced by a path of length exactly $\ell_i$. We also give a family of examples showing that a linear additive term in $h$ is necessary in general.

math.CO↗

arXiv2026

Nearly balanced spanning subdivisions in dense digraphs

Pavez-Sign\'e [Combin. Probab. Comput. 33 (2024), 121--128] conjectured a Dirac-type condition for spanning $H$-subdivisions and asked whether the subdivision paths can additionally be required to have similar lengths. Lee [European J. Combin. 124 (2025), 104059] resolved the existence conjecture in the stronger setting of digraphs. We answer the length-control question in this stronger directed setting: for every $\varepsilon>0$, there exists a constant $C_0>0$ such that, for every digraph $H$ with $h$ arcs and no isolated vertices, every $n$-vertex digraph $D$ with $n\ge C_0h$ and $\delta^0(D)\ge(1/2+\varepsilon)n$ contains a spanning $H$-subdivision whose subdivision paths have lengths differing by at most one.

math.CO↗

arXiv2026

Sparse spanning $k$-strong oriented subdigraphs in split digraphs

Jackson and Thomassen conjectured that every $2k$-strong digraph admits a spanning $k$-strong oriented subdigraph [Ann. N. Y. Acad. Sci. 555 (1989) 402-412]. The conjecture holds for $k=1$ but other than some partial results that have been obtained for general $k$ in some special families of digraphs, including symmetric digraphs, the conjecture remains wide open in general. Even the existence of an integer $K$ such that every $K$-strong digraph has a 2-strong spanning oriented subdigraph is open. As a natural optimization counterpart, the minimum spanning $k$-strong subdigraph (MSSS$_k$) problem, is to find the minimum number of arcs in a spanning $k$-strong subdigraph of a $k$-strong digraph. This problem is NP-hard already for $k=1$ as it generalizes the hamiltonian cycle problem. In this paper, we address both problems simultaneously for the class of split digraphs, by constructing sparse spanning $k$-strong oriented subdigraphs. Specifically, we prove that every $k$-strong split digraph $D = (V_1, V_2; A)$ with minimum semi-degree {$\delta^0(D)\geq 26k+15$} contains a spanning $k$-strong oriented subdigraph with no more than $kn+k|V_1|+98k^2+38k+3$ arcs, where $kn + k|V_1|$ is tight and the $k^{2}$ term is tight up to a constant factor. For the class of $k$-strong tournaments with minimum semi-degree at least $26k+15$ our results improve the bound obtained by Kang in [Combin. Probab. Comput., 27:892-907, 2018].

math.CO↗

arXiv2026

An Exact Dominant Degree Condition for Transitive Tournament Factors in Digraphs

Let $r\ge2$, let $T_r$ denote the transitive tournament on $r$ vertices, and write $d_G^*(v):=\max\{d_G^+(v),d_G^-(v)\}$. We prove that if $r\mid n$ and an $n$-vertex digraph $G$ satisfies $d_G^*(x)+d_G^*(y)\ge 2(1-1/r)n-1$ for every $x\ne y \in V(G)$ with $xy \notin E(G)$, then $G$ has a $T_r$-factor, and the bound is best possible. Furthermore, by applying our main theorem, we settle Treglown's conjecture on the dominant degree $d^*_G(x) \ge (1-1/r)n$ and answer Molla and Treglown's problem of determining the exact Ore-type threshold $2(1-1/r)n - 1$, and we obtain stronger versions of the theorems of Czygrinow, DeBiasio, Kierstead and Molla.

math.CO↗

arXiv2026

K-Arc-Strong Orientations Of Semicomplete Digraphs

Results by Jackson and Frank imply that every 2k-arc-strong digraph D contains a spanning k-arc-strong oriented subdigraph. This is best possible, even for very dense digraphs. A digraph is semicomplete if at least one of the arcs xy,yx is present for every pair of distinct vertices x,y. A tournament has exactly one of xy,yx for every such pair. Clearly every semicomplete digraph D contains a spanning tournament T which is obtained by deleting one arc from every 2-cycle of D. We prove that every (2k-1)-arc-strong semicomplete digraph on at least 2k+1 vertices contains a spanning k-arc-strong tournament. Both bounds 2k-1 and 2k+1 are best possible. The proof uses Frank's general orientation theorem for graphs as well as counting arguments based on the semicomplete structure.

math.CO↗

arXiv2026

Highly connected spanning oriented subdigraphs in generalizations of semicomplete digraphs

Let $k$ be a positive integer. Jackson and Thomassen conjectured in 1989 that there exists an integer function $f(k)$ such that every $f(k)$-strong digraph admits a spanning $k$-strong oriented subdigraph. They even conjectured that one can take $f(k)=2k$ [Ann. N. Y. Acad. Sci. 555 (1989) 402-412]. Already the existence of $f(2)$ is open for general digraphs. Thomassen proved that $f(2)=4$ for symmetric digraphs. For general $k$, the existence of $f(k)$ was only known for locally semicomplete digraphs and quasi-transitive digraphs. Guo proved that every ${(3k-2)}$-strong locally semicomplete digraph contains a spanning $k$-strong local tournament [Discrete Appl. Math. 79 (1997) 119--125]. One can deduce from Guo's result that we have $f(k)\leq 3k-2$ for quasi-transitive digraphs. In this paper, we prove the existence of $f(k)$ for two subclasses of the semicomplete multipartite digraphs, namely extended semicomplete digraphs and semicomplete split digraphs. We prove that every $(4k+1)$-strong extended semicomplete digraph contains a spanning $k$-strong oriented subdigraph and every $5k$-strong semicomplete split digraph contains a spanning $k$-strong oriented subdigraph. The first result implies that for the large class of digraphs which can be obtained from some semicomplete digraph $S$ on at least 3 vertices by substituting arbitrary digraphs for each vertex of $S$ we also have $f(k)\leq 4k+1$.

math.CO↗

arXiv2026

The exact total degree threshold for the square of a Hamilton cycle in digraphs

The P\'{o}sa-Seymour conjecture establishes the minimum degree threshold required to guarantee the presence of the $k$th power of a Hamilton cycle in a graph. Following numerous partial results, Koml\'{o}s, S\'{a}rk\"{o}zy, and Szemer\'{e}di confirmed the conjecture holds for all sufficiently large graphs. Treglown later conjectured the analogous minimum semi-degree threshold for forcing the $k$th power of a Hamilton cycle in a digraph. Subsequently, DeBiasio et al. proposed a conjecture on the minimum total degree threshold for the same problem. In this paper we settle the conjecture of DeBiasio et al. for $k=2$. Specifically, we prove that every sufficiently large $n$-vertex digraph with minimum total degree at least $8n/5-c$ contains the square of a Hamilton cycle, where $c=2$ if $n\equiv2,4\pmod 5$, and $c=1$ otherwise.

math.CO↗

arXiv2026

Polynomial Algorithms for Minimum Degree Partitions in Semicomplete Digraphs

A 2-partition of a digraph is a partition of its vertex set into two nonempty parts. Degree-constrained 2-partition problems are generally computationally difficult, even when the prescribed properties are expressed only in terms of minimum indegree, minimum outdegree, or minimum semidegree. Bang-Jensen and Christiansen~\cite{B-C} conjectured that the minimum-degree partition problems would be polynomial-time solvable on semicomplete digraphs when the degree thresholds are fixed, and Bang-Jensen and Gutin~\cite{B-G-Classes} posed the related Problems~2.8.15 and~2.8.16. We resolve this conjecture. More precisely, for every fixed pair of integers $k_1,k_2\ge 2$, we give deterministic polynomial-time algorithms that decide whether a given semicomplete digraph admits a $(\delta^+\geq k_1,\delta^-\geq k_2)$-partition, a $(\delta^+\geq k_1,\delta^0\geq k_2)$-partition, or a $(\delta^0\geq k_1,\delta^0\geq k_2)$-partition, and construct such a partition whenever one exists. Here, $\delta ^+,\delta ^-,\delta ^0$ represent the minimum out-, in-, semi-degree, respectively. The algorithms use small degree certificates, minimal cores, closure and protective-set arguments, and deterministic universal colorings with monotone recoloring, which develop a new method in partition algorithm construction.

cs.DM↗

arXiv2026

Investigation of regional variations in CO$_2$ growth rates : Integrating Emission Inventories and Atmospheric Observations

Atmospheric carbon dioxide (CO2) growth rates reflects the combined influence of anthropogenic emissions, biospheric carbon exchange, and climate variability. While climate mitigation is primarily evaluated using bottom-up emission inventories within political boundaries, there is a need to validate these emission reductions using atmospheric measurements. Here, we present a global top-down analysis of atmospheric CO2 growth rates using CAMS atmospheric CO2 reanalysis, EDGAR anthropogenic emissions, GOSIF dataset and the Southern Oscillation Index (SOI) as a measures of biospheric activity, to quantify the relative influence of human and natural drivers. We find that atmospheric CO2 growth rate varies substantially across space and time but is dominated by natural carbon-cycle processes and global background trends. Anthropogenic emission signals are frequently masked by natural variability, making regional top-down detection of human emission changes difficult. The COVID-19 emission reductions in 2020, despite occurring during a neutral ENSO year, were not consistently reflected in regional atmospheric CO2 growth rates, highlighting the dominant roles of biospheric dynamics and atmospheric transport. Using unsupervised clustering and persistence analysis, we identify five characteristic carbon-cycle regimes. Spatial averaging removes much of the regional variability, leaving large-scale climate as the dominant control in most regimes. The active biosphere is the main exception, where strong biogenic signals persist, underscoring the critical role of tropical forests in shaping atmospheric CO2 variability.

physics.ao-ph↗