Zobrazeno 1 - 10
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pro vyhledávání: '"Deschamps, Quentin"'
The metric dimension has been introduced independently by Harary, Melter and Slater in 1975 to identify vertices of a graph G using its distances to a subset of vertices of G. A resolving set X of a graph G is a subset of vertices such that, for ever
Externí odkaz:
http://arxiv.org/abs/2303.10646
Autor:
Bagan, Guillaume, Deschamps, Quentin, Duchêne, Eric, Durain, Bastien, Effantin, Brice, Gledel, Valentin, Oijid, Nacim, Parreau, Aline
Positional games have been introduced by Hales and Jewett in 1963 and have been extensively investigated in the literature since then. These games are played on a hypergraph where two players alternately select an unclaimed vertex of it. In the Maker
Externí odkaz:
http://arxiv.org/abs/2211.01083
Autor:
Corsini, Timothée, Deschamps, Quentin, Feghali, Carl, Gonçalves, Daniel, Langlois, Hélène, Talon, Alexandre
Let $G$ be a connected graph with maximum degree $\Delta \geq 3$ distinct from $K_{\Delta + 1}$. Generalizing Brooks' Theorem, Borodin, Kostochka and Toft proved that if $p_1, \dots, p_s$ are non-negative integers such that $p_1 + \dots + p_s \geq \D
Externí odkaz:
http://arxiv.org/abs/2204.11100
The discharging method is a powerful proof technique, especially for graph coloring problems. Its major downside is that it often requires lengthy case analyses, which are sometimes given to a computer for verification. However, it is much less commo
Externí odkaz:
http://arxiv.org/abs/2204.05791
Autor:
Bagan, Guillaume, Deschamps, Quentin, Duchêne, Eric, Durain, Bastien, Effantin, Brice, Gledel, Valentin, Oijid, Nacim, Parreau, Aline
Publikováno v:
In Discrete Mathematics August 2024 347(8)
Autor:
Deschamps, Quentin, Feghali, Carl, Kardoš, František, Legrand-Duchesne, Clément, Pierron, Théo
For an integer $k \geq 1$ and a graph $G$, let $\mathcal{K}_k(G)$ be the graph that has vertex set all proper $k$-colorings of $G$, and an edge between two vertices $\alpha$ and~$\beta$ whenever the coloring~$\beta$ can be obtained from $\alpha$ by a
Externí odkaz:
http://arxiv.org/abs/2201.07595
Square coloring is a variant of graph coloring where vertices within distance two must receive different colors. When considering planar graphs, the most famous conjecture (Wegner, 1977) states that $\frac32\Delta+1$ colors are sufficient to square c
Externí odkaz:
http://arxiv.org/abs/2112.12512
A locating-dominating set in an undirected graph is a subset of vertices $S$ such that $S$ is dominating and for every $u,v \notin S$, we have $N(u)\cap S\ne N(v)\cap S$. In this paper, we consider the oriented version of the problem. A locating-domi
Externí odkaz:
http://arxiv.org/abs/2112.01910
The metric dimension dim(G) of a graph $G$ is the minimum cardinality of a subset $S$ of vertices of $G$ such that each vertex of $G$ is uniquely determined by its distances to $S$. It is well-known that the metric dimension of a graph can be drastic
Externí odkaz:
http://arxiv.org/abs/2111.07845
Autor:
Corsini, Timothée, Deschamps, Quentin, Feghali, Carl, Gonçalves, Daniel, Langlois, Hélène, Talon, Alexandre
Publikováno v:
In European Journal of Combinatorics December 2023 114