The star and biclique coloring and choosability problems

A biclique of a graph G is an induced complete bipartite graph. A star of G is a biclique contained in the closed neighborhood of a vertex. A star (biclique) k-coloring of G is a k-coloring of G that contains no monochromatic maximal stars (bicliques). Similarly, for a list assignment L of G, a star...

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Autor principal: Groshaus, M.
Otros Autores: Soulignac, F.J, Terlisky, P.
Formato: Capítulo de libro
Lenguaje:Inglés
Publicado: Brown University 2014
Acceso en línea:Registro en Scopus
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245 1 4 |a The star and biclique coloring and choosability problems 
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520 3 |a A biclique of a graph G is an induced complete bipartite graph. A star of G is a biclique contained in the closed neighborhood of a vertex. A star (biclique) k-coloring of G is a k-coloring of G that contains no monochromatic maximal stars (bicliques). Similarly, for a list assignment L of G, a star (biclique) L-coloring is an L-coloring of G in which no maximal star (biclique) is monochromatic. If G admits a star (biclique) L- coloring for every k-list assignment L, then G is said to be star (biclique) k-choosable. In this article we study the computational complexity of the star and biclique coloring and choosability problems. Specifically, we prove that the star (biclique) k-coloring and k-choosability problems are Σp2-complete and IIp3-complete for k > 2, respectively, even when the input graph contains no induced C4 or Kk+2. Then, we study all these problems in some related classes of graphs, including H-free graphs for every H on three vertices, graphs with restricted diamonds, split graphs, and threshold graphs.  |l eng 
593 |a Departamento de Computación, FCEN, Universidad de Buenos Aires, Buenos Aires, Argentina 
593 |a CONICET, Argentina 
593 |a Universidad Nacional de Quilmes, Buenos Aires, Argentina 
700 1 |a Soulignac, F.J. 
700 1 |a Terlisky, P. 
773 0 |d Brown University, 2014  |g v. 18  |h pp. 347-383  |k n. 3  |p J. Graph Algorithms and Appl.  |x 15261719  |w (AR-BaUEN)CENRE-8790  |t Journal of Graph Algorithms and Applications 
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