Zobrazeno 1 - 10
of 869
pro vyhledávání: '"05c31"'
Autor:
Lerner, E. Yu.
Given a simple biconnected planar cubic graph, we associate each its vertex among $2n$ ones with the so-called spin, i.e., a variable which takes on values $\pm 1$. P. J. Heawood has proved that a Tait coloring, accurate to the choice of a color for
Externí odkaz:
http://arxiv.org/abs/2411.15992
Autor:
Hlushchanka, Mikhail, Peters, Han
We study the zero sets of the independence polynomial on recursive sequences of graphs. We prove that for a maximally independent starting graph and a stable and expanding recursion algorithm, the zeros of the independence polynomial are uniformly bo
Externí odkaz:
http://arxiv.org/abs/2411.14791
Publikováno v:
American Journal of Combinatorics, 3:35-43, (2024)
Let $G$ be a bipartite graph with adjacency matrix $A(G)$. The characteristic polynomial $\phi(G,x)=\det(xI-A(G))$ and the permanental polynomial $\pi(G,x) = \text{per}(xI-A(G))$ are both graph invariants used to distinguish graphs. For bipartite gra
Externí odkaz:
http://arxiv.org/abs/2411.14238
In this paper, we examine roots of graph polynomials where those roots can be considered as structural graph measures. More precisely, we prove analytical results for the roots of certain modified graph polynomials and also discuss numerical results.
Externí odkaz:
http://arxiv.org/abs/2411.05513
Autor:
Bérczi, Gergely, Klüver, Jonas
We propose a conjectural counting formula for the coefficients of the chromatic symmetric function of unit interval graphs using reinforcement learning. The formula counts specific disjoint cycle-tuples in the graphs, referred to as Eschers, which sa
Externí odkaz:
http://arxiv.org/abs/2410.19189
We assign a new polynomial to any checkerboard-colorable 4-valent virtual graph in terms of its Euler circuit expansion. This provides a new combinatorial formulation of the Kauffman-Jones polynomial for checkerboard-colorable virtual links.
Com
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Externí odkaz:
http://arxiv.org/abs/2410.15574
Zonotopal algebras (external, central, and internal) of an undirected graph G introduced by Postnikov-Shapiro and Holtz-Ron, are finite-dimensional commutative graded algebras whose Hilbert series contain a wealth of combinatorial information about G
Externí odkaz:
http://arxiv.org/abs/2407.19431
Autor:
Nishimura, Yusaku
R.P. Stanley defined a invariant for graphs called the chromatic symmetric function and conjectured it is complete invariant for trees. Miezaki et al. generalised the chromatic symmetric function and defined the Kneser chromatic functions denoted by
Externí odkaz:
http://arxiv.org/abs/2409.20478
Autor:
Kálmán, Tamás, Tóthmérész, Lilla
We study the extended root polytope associated to a directed graph. We show that under the operations of deletion and contraction of an edge of the digraph, none of the coefficients of the $h^*$-polynomial of its associated lattice polytope will incr
Externí odkaz:
http://arxiv.org/abs/2409.18902
The purpose of the present paper is to provide, for all pairs of integers $(\Delta,g)$ with $\D\ge 3$ and $g\ge 3$, a positive number $C(\Delta, g)$ such that chromatic polynomial $P_G(q)$ of a graph $G$ with maximum degree $\Delta$ and finite girth
Externí odkaz:
http://arxiv.org/abs/2409.13892