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Unified Approach to Polynomial Algorithms on Graphs of Bounded (bi-)Rank-width

Název česky Sjednocený přístup k polynomiálním algoritmům na grafech omezené rank-width
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GANIAN Robert HLINĚNÝ Petr OBDRŽÁLEK Jan

Druh Článek v odborném periodiku
Časopis / Zdroj European Journal of Combinatorics
Fakulta / Pracoviště MU

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Citace
Doi http://dx.doi.org/10.1016/j.ejc.2012.07.024
Obor Informatika
Klíčová slova rank-width; XP algorithm; coloring
Popis In this paper we develop new algorithmic machinery for solving hard problems on graphs of bounded rank-width and on digraphs of bounded bi-rank-width in polynomial (XP, to be precise) time. These include, particularly, graph coloring and chromatic polynomial problems, the Hamiltonian path and c-min-leaf outbranching, the directed cut, and more generally MSOL-partitioning problems on digraphs. Our focus on a formally clean and unified approach for the considered algorithmic problems is in contrast with many previous published XP algorithms running on graphs of bounded clique-width, which mostly used ad hoc techniques and ideas. The new contributions include faster algorithms for computing the chromatic number and the chromatic polynomial on graphs of bounded rank-width, and new algorithms for solving the defective coloring, the min-leaf outbranching, and the directed cut problems.
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