Biclique-colouring verification complexity and biclique-colouring power graphs
نویسندگان
چکیده
منابع مشابه
Biclique-colouring verification complexity and biclique-colouring power graphs
Biclique-colouring is a colouring of the vertices of a graph in such a way that no maximal complete bipartite subgraph with at least one edge is monochromatic. We show that it is coNP-complete to check whether a given function that associates a colour to each vertex is a bicliquecolouring, a result that justifies the search for structured classes where the biclique-colouring problem could be ef...
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A biclique of a graph G is a maximal induced complete bipartite subgraph of G. Given a graph G, the biclique matrix of G is a {0,1,−1} matrix having one row for each biclique and one column for each vertex of G, and such that a pair of 1, −1 entries in a same row corresponds exactly to adjacent vertices in the corresponding biclique. We describe a characterization of biclique matrices, in simil...
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A biclique is a set of vertices that induce a bipartite complete graph. A graph G is biclique-Helly when its family of maximal bicliques satisfies the Helly property. If every induced subgraph of G is also biclique-Helly, then G is hereditary biclique-Helly. A graph is C4-dominated when every cycle of length 4 contains a vertex that is dominated by the vertex of the cycle that is not adjacent t...
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A graph G is chordless if no cycle in G has a chord. In the present work we investigate the chromatic index and total chromatic number of chordless graphs. We describe a known decomposition result for chordless graphs and use it to establish that every chordless graph of maximum degree ∆ ≥ 3 has chromatic index ∆ and total chromatic number ∆+1. The proofs are algorithmic in the sense that we ac...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2015
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.05.001