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The dichromatic number of a digraph $D$ is the minimum number of colors of a vertex coloring of $D$ such that $D$ has no monochromatic cycles. The Haj\'os join were recently extended to digraphs (using the dichromatic number) by J. Bang-Jensen et. al
Externí odkaz:
http://arxiv.org/abs/2301.07181
Publikováno v:
Discrete Mathematics & Theoretical Computer Science, vol. 25:1, Discrete Algorithms (March 1, 2023) dmtcs:10189
In 2020 Bang-Jensen et. al. generalized the Haj\'os join of two graphs to the class of digraphs and generalized several results for vertex colorings in digraphs. Although, as a consequence of these results, a digraph can be obtained by Haj\'os constr
Externí odkaz:
http://arxiv.org/abs/2210.05080
Autor:
Araujo-Pardo, Gabriela, Montellano-Ballesteros, Juan José, Olsen, Mika, Rubio-Montiel, Christian
The harmonious chromatic number of a graph $G$ is the minimum number of colors that can be assigned to the vertices of $G$ in a proper way such that any two distinct edges have different color pairs. This paper gives various results on harmonious chr
Externí odkaz:
http://arxiv.org/abs/2206.04822
The dichromatic number and the diachromatic number are generalizations of the chromatic number and the achromatic number for digraphs considering acyclic colorings. In this paper, we determine the diachromatic number of digraphs arising from the Zyko
Externí odkaz:
http://arxiv.org/abs/2201.12410
Autor:
Araujo-Pardo, Gabriela, Montellano-Ballesteros, Juan José, Olsen, Mika, Rubio-Montiel, Christian
We extend the Grundy number and the ochromatic number, parameters on graph colorings, to digraph colorings, we call them {\emph{digrundy number}} and {\emph{diochromatic number}}, respectively. First, we prove that for every digraph the diochromatic
Externí odkaz:
http://arxiv.org/abs/2103.11917
We consider the following problem posed by Volkmann in 2007: How close to regular must a c-partite tournament be, to secure a strongly connected subtournament of order $c$? We give sufficient conditions on the regularity of balanced $c$-partite tourn
Externí odkaz:
http://arxiv.org/abs/2010.09835
Autor:
Araujo-Pardo, Gabriela, Montellano-Ballesteros, Juan Jos{\' e}, Olsen, Mika, Rubio-Montiel, Christian
In this paper, we determine the achromatic and diachromatic numbers of some circulant graphs and digraphs each one with two lengths and give bounds for other circulant graphs and digraphs with two lengths. In particular, for the achromatic number we
Externí odkaz:
http://arxiv.org/abs/1912.10104
The \emph{packing chromatic number $\chi_\rho (G)$} of a graph $G$ is the smallest integer $k$ for which there exists a vertex coloring $\Gamma: V(G)\rightarrow \{1,2,\dots , k\}$ such that any two vertices of color $i$ are at distance at least $i +
Externí odkaz:
http://arxiv.org/abs/1909.11638
Publikováno v:
In Discrete Mathematics July 2023 346(7)
Publikováno v:
In Procedia Computer Science 2023 223:112-120