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Disproving the normal graph conjecture
Journal of Combinatorial Theory Series B ( IF 1.2 ) Pub Date : 2020-04-16 , DOI: 10.1016/j.jctb.2020.04.001 Ararat Harutyunyan , Lucas Pastor , Stéphan Thomassé
中文翻译:
证明法线图猜想
更新日期:2020-04-21
Journal of Combinatorial Theory Series B ( IF 1.2 ) Pub Date : 2020-04-16 , DOI: 10.1016/j.jctb.2020.04.001 Ararat Harutyunyan , Lucas Pastor , Stéphan Thomassé
A graph G is called normal if there exist two coverings, and of its vertex set such that every member of induces a clique in G, every member of induces an independent set in G and for every and . It has been conjectured by De Simone and Körner in 1999 that a graph G is normal if G does not contain , and as an induced subgraph. We disprove this conjecture.
中文翻译:
证明法线图猜想
如果存在两个覆盖,则图G称为法线, 和 的顶点集 诱导一个集团ģ,的每一个成员诱导一组独立的g ^和 每一个 和 。它于1999年被臆想由De Simone和克尔纳一个图形摹是正常的,如果摹不含, 和 作为诱导子图。我们反对这一猜想。