On strongly planar not-all-equal 3SAT

Ali Dehghan ()
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Ali Dehghan: Amirkabir University of Technology

Journal of Combinatorial Optimization, 2016, vol. 32, issue 3, No 4, 724 pages

Abstract: Abstract In this paper we show that there is a polynomial time algorithm for the strongly planar not-all-equal 3SAT problem. Also, we prove that a restricted version of planar not-all-equal 3SAT is $$ \mathbf {NP} $$ NP -complete and in consequence of this result, we show that for a given planar bipartite graph $$G$$ G , deciding whether there is a vertex-labeling by gap from $$\{1,2\}$$ { 1 , 2 } such that the induced proper coloring is a proper vertex 2-coloring is $$ \mathbf {NP} $$ NP -complete.

Keywords: Strongly planar 3SAT; Strongly planar not-all-equal 3SAT; Vertex-labeling by gap (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10878-015-9894-6

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