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- W2570586226 abstract "AbstractLet χ(G) denote the chromatic number of a graph G. A colored set of vertices of G is called forcing if its coloring is extendable to a proper χ(G)-coloring of the whole graph in a unique way. The forcing chromatic number F χ (G) is the smallest cardinality of a forcing set of G. We estimate the computational complexity of F χ (G) relating it to the complexity class US introduced by Blass and Gurevich. We prove that recognizing if F χ (G) ≤ 2 is US-hard with respect to polynomial-time many-one reductions. Furthermore, this problem is coNP-hard even under the promises that F χ (G) ≤ 3 and G is 3-chromatic. On the other hand, recognizing if F χ (G) ≤ k, for each constant k, is reducible to a problem in US via a disjunctive truth-table reduction. Similar results are obtained also for forcing variants of the clique and the domination numbers of a graph.KeywordsComputational ComplexityConnected GraphChromatic NumberDomination NumberMinimum CardinalityThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
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- W2570586226 date "2005-01-01" @default.
- W2570586226 modified "2023-09-26" @default.
- W2570586226 title "On the Computational Complexity of the Forcing Chromatic Number" @default.
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- W2570586226 doi "https://doi.org/10.1007/978-3-540-31856-9_15" @default.
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