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- W78920299 abstract "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 co NP -complete to check whether a given function that associates a colour to each vertex is a biclique-colouring, a result that justifies the search for structured classes where the biclique-colouring problem could be efficiently solved. We consider biclique-colouring restricted to powers of paths and powers of cycles. We determine the biclique-chromatic number of powers of paths and powers of cycles. The biclique-chromatic number of a power of a path P n k is max ( 2 k + 2 − n , 2 ) if n ≥ k + 1 and exactly n otherwise. The biclique-chromatic number of a power of a cycle C n k is at most 3 if n ≥ 2 k + 2 and exactly n otherwise; we additionally determine the powers of cycles that are 2-biclique-colourable. All proofs are algorithmic and provide polynomial-time biclique-colouring algorithms for graphs in the investigated classes." @default.
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- W78920299 date "2015-09-01" @default.
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- W78920299 title "Biclique-colouring verification complexity and biclique-colouring power graphs" @default.
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- W78920299 doi "https://doi.org/10.1016/j.dam.2014.05.001" @default.
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