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Pré-Publication, Document De Travail Année : 2015

Analogous to cliques of (m,n)-colored mixed graphs

Résumé

A (m,n)-colored mixed graph is a graph having arcs of m different colors and edges of n di fferent colors. A graph homomorphism of a (m,n)-colored mixed graph G to a (m,n)-colored mixed graph H is a vertex mapping such that if uv is an arc (edge) of color c in G, then f(u)f(v) is also an arc (edge) of color c. The (m,n)-colored mixed chromatic number chi(m,n)(G) of a (m,n)-colored mixed graph G, introduced by Nesetril and Raspaud, is the order (number of vertices) of the smallest homomorphic image of G. In this article, we de ne the analogue of clique for (m,n)-colored mixed graphs. A (m,n)-clique is a (m,n)-colored mixed graph C with (m,n)(C) = |C|. We show that almost all (m,n)-colored mixed graphs are (m,n)-cliques. We prove exact bound on the order of the biggest outerplanar (m,n)-clique and provide upper and lower bounds for the order of the biggest planar (m,n)-clique. Furthermore, we address a particular complexity problem related to (0,2)-colored mixed graphs and compare the parameters (1,0) and (0,2).
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Dates et versions

hal-01078218 , version 1 (28-10-2014)
hal-01078218 , version 2 (20-05-2015)
hal-01078218 , version 3 (07-11-2017)

Identifiants

  • HAL Id : hal-01078218 , version 2

Citer

Julien Bensmail, Christopher Duffy, Sagnik Sen. Analogous to cliques of (m,n)-colored mixed graphs. 2015. ⟨hal-01078218v2⟩
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