Fixed points in conjunctive networks and maximal independent sets in graph contractions

Abstract : Given a graph G, viewed as a loop-less symmetric digraph, we study the maximum number of fixed points in a conjunctive boolean network with G as interaction graph. We prove that if G has no induced C 4 , then this quantity equals both the number of maximal independent sets in G and the maximum number of maximal independent sets among all the graphs obtained from G by contracting some edges. We also prove that, in the general case, it is coNP-hard to decide if one of these equalities holds, even if G has a unique induced C 4 .
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Julio Aracena, Adrien Richard, Lilian Salinas. Fixed points in conjunctive networks and maximal independent sets in graph contractions. Journal of Computer and System Sciences, Elsevier, 2017, 88, pp.145-163. ⟨10.1016/j.jcss.2017.03.016⟩. ⟨hal-01630474⟩

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