Zobrazeno 1 - 10
of 3 362
pro vyhledávání: '"05C05"'
Autor:
Kundu, Debanjana, Müller, Katharina
In this article, we study questions pertaining to ramified $\mathbb{Z}_p^d$-extensions of a finite connected graph $X$. We also study the Iwasawa theory of dual graphs.
Externí odkaz:
http://arxiv.org/abs/2410.11704
Autor:
Devriendt, Karel
This article introduces and studies a new class of graphs motivated by discrete curvature. We call a graph resistance nonnegative if there exists a distribution on its spanning trees such that every vertex has expected degree at most two in a random
Externí odkaz:
http://arxiv.org/abs/2410.07756
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:
Ai, Jiangdong, Ellingham, M. N., Gao, Zhipeng, Huang, Yixuan, Liu, Xiangzhou, Shan, Songling, Špacapan, Simon, Yue, Jun
Let $G$ be a graph (with multiple edges allowed) and let $T$ be a tree in $G$. We say that $T$ is $\textit{even}$ if every leaf of $T$ belongs to the same part of the bipartition of $T$, and that $T$ is $\textit{weakly even}$ if every leaf of $T$ tha
Externí odkaz:
http://arxiv.org/abs/2409.15522
Autor:
Pokrovskiy, Alexey
A rough structure theorem is proved for graphs $G$ containing no copy of a bounded degree tree $T$: from any such $G$, one can delete $o(|G||T|)$ edges in order to get a subgraph all of whose connected components have a cover of order $3|T|$. This th
Externí odkaz:
http://arxiv.org/abs/2409.15191
Autor:
Pokrovskiy, Alexey
This is a companion paper to the paper "Hyperstability in the Erdos-Sos Conjecture". In that paper the following rough structure theorem was proved for graphs G containing no copy of a bounded degree tree T: from any such G, one can delete o(|G||T|)
Externí odkaz:
http://arxiv.org/abs/2409.15189
Autor:
Finch, Steven
We treat three cubic recurrences, two of which generalize the famous iterated map $x \mapsto x (1-x)$ from discrete chaos theory. A feature of each asymptotic series developed here is a constant, dependent on the initial condition but otherwise intri
Externí odkaz:
http://arxiv.org/abs/2409.15175
Given a graph $G$ and a family of graphs $\cal F$, an $\cal F$-isolating set, as introduced by Caro and Hansberg, is any set $S\subset V(G)$ such that $G - N[S]$ contains no member of $\cal F$ as a subgraph. In this paper, we introduce a game in whic
Externí odkaz:
http://arxiv.org/abs/2409.14180
We consider a Gibbs distribution over all spanning trees of an undirected, edge weighted finite graph, where, up to normalization, the probability of each tree is given by the product of its edge weights. Defining the weighted degree of a node as the
Externí odkaz:
http://arxiv.org/abs/2409.13472
Autor:
Tom, Foster
We prove that a tree with a vertex of degree at least five must be missing a connected partition of some type and therefore its chromatic symmetric function cannot be $e$-positive. We prove that this also holds for a tree with a vertex of degree four
Externí odkaz:
http://arxiv.org/abs/2409.12934