Zobrazeno 1 - 10
of 112
pro vyhledávání: '"05C35, 05C69"'
We define various notions of energy of a set of vertices in a graph, which generalize two of the most widely studied graphical indices: the Wiener index and the Harary index. We prove several theorems indicating that these notions of energy can be us
Externí odkaz:
http://arxiv.org/abs/2407.18785
Autor:
Borg, Peter
A copy of a graph $F$ is called an $F$-copy. For any graph $G$, the $F$-isolation number of $G$, denoted by $\iota(G,F)$, is the size of a smallest subset $D$ of the vertex set of $G$ such that the closed neighbourhood $N[D]$ of $D$ in $G$ intersects
Externí odkaz:
http://arxiv.org/abs/2407.18126
Given integers $\Delta\ge 2$ and $t\ge 2\Delta$, suppose there is a graph of maximum degree $\Delta$ and a partition of its vertices into blocks of size at least $t$. By a seminal result of Haxell, there must be some independent set of the graph that
Externí odkaz:
http://arxiv.org/abs/2407.04367
Autor:
Cambie, Stijn
We explore the question asking for graphs $G$ for which the total distance decreases, possibly by a fixed constant $k$, upon the removal of any of its vertices. We obtain results leading to intuition and doubts for the \v{S}olt\'es' problem ($k=0$) a
Externí odkaz:
http://arxiv.org/abs/2406.03451
Autor:
Devlin, Pat, Douhovnikoff, Leo
We study the diametric problem (i.e., optimal anticodes) in the space of permutations under the Ulam distance. That is, let $S_n$ denote the set of permutations on $n$ symbols, and for each $\sigma, \tau \in S_n$, define their Ulam distance as the nu
Externí odkaz:
http://arxiv.org/abs/2403.02276
Let $p$ be a prime and $q = p^k$. A subset $\mathcal{F} \subset \operatorname{\Gamma L}_{2}(q)$ is intersecting if any two semilinear transformations in $\mathcal{F}$ agree on some non-zero vector in $\mathbb{F}_q^2$. We show that any intersecting se
Externí odkaz:
http://arxiv.org/abs/2402.17687
One of Thomassen's classical results is that every planar graph of girth at least $5$ is 3-choosable. One can wonder if for a planar graph $G$ of girth sufficiently large and a $3$-list-assignment $L$, one can do even better. Can one find $3$ disjoin
Externí odkaz:
http://arxiv.org/abs/2312.17233
Autor:
Cambie, Stijn, Jooken, Jorik
The occupancy fraction of a graph is a (normalized) measure on the size of independent sets under the hard-core model, depending on a variable (fugacity) $\lambda.$ We present a criterion for finding the graph with minimum occupancy fraction among gr
Externí odkaz:
http://arxiv.org/abs/2311.05542
The \emph{intersection density} of a finite transitive group $G\leq \operatorname{Sym}(\Omega)$ is the rational number $\rho(G)$ given by the ratio between the maximum size of a subset of $G$ in which any two permutations agree on some elements of $\
Externí odkaz:
http://arxiv.org/abs/2309.09906
Let $\mathrm{ex}(n,s)$ denote the maximum number of edges in a triangle-free graph on $n$ vertices which contains no independent sets larger than $s$. The behaviour of $\mathrm{ex}(n,s)$ was first studied by Andr\'asfai, who conjectured that for $s>n
Externí odkaz:
http://arxiv.org/abs/2308.06070