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发表于 2025-3-28 16:32:14 | 显示全部楼层
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The maximal ,-dependent set problem for planar graphs is in NC,d a maximal subset . of . such that no vertex . has degree>.(.) in the subgraph induced by .. Whether the problem is in . (or .) or not is an open question. Concerning this question, only a rather trivial result due to Diks, Garrido, and Lingas is known up to now, which says that the problem can be
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Dominoes,ow that they can be recognized in linear time, give a linear time algorithm for listing all maximal cliques (which implies a linear time algorithm computing a maximum clique of a domino) and show that the PATHWIDTH problem remains NP-complete when restricted to the class of chordal dominoes.
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Minimum vertex cover, distributed decision-making, and communication complexity,re . is the number of processors. In the second framework two processors are allowed to communicate in order to find an approximate solution: in this latter case, we show a linear lower bound on the communication complexity of the problem.
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https://doi.org/10.1007/978-2-8178-0466-8bstruction of order .+2 for width ., we find that the number of obstructions of order .+3 alone is an asymptotically exponential function of .. Our proof of this is based on the theory of partitions of integers and is the first non-trivial lower bound on the number of obstructions for treewidth.
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