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pro vyhledávání: '"Dettlaff Magda"'
Let $G$ be a graph and c a proper k-coloring of G, i.e. any two adjacent vertices u and v have different colors c(u) and c(v). A proper k-coloring is a b-coloring if there exists a vertex in every color class that contains all the colors in its close
Externí odkaz:
http://arxiv.org/abs/2311.13283
A graph is $\alpha$-excellent if every vertex of the graph is contained in some maximum independent set of the graph. In this paper, we present two characterizations of the $\alpha$-excellent $2$-trees.
Comment: 10 pages, 3 figures
Comment: 10 pages, 3 figures
Externí odkaz:
http://arxiv.org/abs/2210.14387
A dominating set in a graph $G$ is a set $S$ of vertices such that every vertex that does not belong to $S$ is adjacent to a vertex in $S$. The domination number $\gamma(G)$ of $G$ is the minimum cardinality of a dominating set of $G$. The common ind
Externí odkaz:
http://arxiv.org/abs/2208.07092
Publikováno v:
In Applied Mathematics and Computation 15 November 2024 481
A subset $D$ of $V$ is \emph{dominating} in $G$ if every vertex of $V-D$ has at least one neighbour in $D;$ let $\gamma(G)$ be the minimum cardinality among all dominating sets in $G.$ A graph $G$ is $\gamma$-$q$-{\it critical} if the smallest subset
Externí odkaz:
http://arxiv.org/abs/2002.05389
Publikováno v:
In Discrete Applied Mathematics 15 January 2024 342:253-259
Given a graph $G=(V(G), E(G))$, the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph $G$ are denoted by $\gamma(G)$, $\gamma_{\rm pr}(G)$, and $\gamma_{t}(G)$, respectively. For a positive
Externí odkaz:
http://arxiv.org/abs/1911.04098
In this paper we study relations between connected and weakly convex domination numbers. We show that in general the difference between these numbers can be arbitrarily large and we focus on the graphs for which a weakly convex domination number equa
Externí odkaz:
http://arxiv.org/abs/1902.07505
Publikováno v:
In Procedia Computer Science 2023 223:385-387
Autor:
Dettlaff, Magda, Lemańska, Magdalena, Miotk, Mateusz, Topp, Jerzy, Ziemann, Radosław, Żyliński, Paweł
A set $D$ of vertices of a graph $G$ is a dominating set of $G$ if every vertex in $V_G-D$ is adjacent to at least one vertex in $D$. The domination number (upper domination number, respectively) of a graph $G$, denoted by $\gamma(G)$ ($\Gamma(G)$, r
Externí odkaz:
http://arxiv.org/abs/1710.02059