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A span of a given graph $G$ is the maximum distance that two players can keep at all times while visiting all vertices (edges) of $G$ and moving according to certain rules, that produce different variants of span. We prove that the vertex and edge sp
Externí odkaz:
http://arxiv.org/abs/2410.19524
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
The Maker-Breaker domination game (MBD game) is a two-player game played on a graph $G$ by Dominator and Staller. They alternately select unplayed vertices of $G$. The goal of Dominator is to form a dominating set with the set of vertices selected by
Externí odkaz:
http://arxiv.org/abs/2408.16297
Given a graph $G$, the maximum size of an induced subgraph of $G$ each component of which is a star is called the edge open packing number, $\rho_{e}^{o}(G)$, of $G$. Similarly, the maximum size of an induced subgraph of $G$ each component of which i
Externí odkaz:
http://arxiv.org/abs/2406.04020
In this follow-up to [M.G.~Cornet, P.~Torres, arXiv:2308.15603], where the $k$-tuple domination number and the 2-packing number in Kneser graphs $K(n,r)$ were studied, we are concerned with two variations, the $k$-domination number, ${\gamma_{k}}(K(n
Externí odkaz:
http://arxiv.org/abs/2312.15464
While a number of bounds are known on the zero forcing number $Z(G)$ of a graph $G$ expressed in terms of the order of a graph and maximum or minimum degree, we present two bounds that are related to the (upper) total domination number $\gamma_t(G)$
Externí odkaz:
http://arxiv.org/abs/2310.07432
Several concepts that model processes of spreading (of information, disease, objects, etc.) in graphs or networks have been studied. In many contexts, we assume that some vertices of a graph $G$ are contaminated initially, before the process starts.
Externí odkaz:
http://arxiv.org/abs/2309.16852
Publikováno v:
In Discrete Applied Mathematics 15 August 2024 353:139-150
Autor:
Brešar, Boštjan, Dravec, Tanja
A set $D$ of vertices of a graph $G$ is a dissociation set if each vertex of $D$ has at most one neighbor in $D$. The dissociation number of $G$, $diss(G)$, is the cardinality of a maximum dissociation set in a graph $G$. In this paper we study disso
Externí odkaz:
http://arxiv.org/abs/2108.10801
Autor:
Akbari, Saieed, Beikmohammadi, Arash, Brešar, Boštjan, Dravec, Tanja, Habibollahi, Mohammad Mahdi, Movarraei, Nazanin
Given a non-trivial graph $G$, the minimum cardinality of a set of edges $F$ in $G$ such that $\chi'(G \setminus F)<\chi'(G)$ is called the chromatic edge stability index of $G$, denoted by $es_{\chi'}(G)$, and such a (smallest) set $F$ is called a (
Externí odkaz:
http://arxiv.org/abs/2108.10657