Abstract
A kernel of a directed graph is a set of vertices which is both independent and absorbent. And a digraph is said to be kernel perfect if and only if any induced subdigraph has a kernel. Given a set of arcs F, a semikernel S modulo F is an independent set such that if some Sz-arc is not in F, then there exists a zS-arc. A sufficient condition on the digraph is given in terms of semikernel modulo F in order to guarantee that a digraph is kernel perfect. To do that we give a characterization of kernel perfectness which is a generalization of a previous result given by Neumann-Lara [Seminúcleos de una digráfica. Anales del Instituto de Matemáticas 2, Universidad Nacional Autónoma de México, 1971]. And moreover, we show by means of an example that our result is independent of previous known sufficient conditions.
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Supported by the Ministry of Education and Science, Spain, and the European Regional Development Fund (ERDF) under projects MTM2008-06620-C03-02 and by the Catalonian Government under project 1298 SGR2009. The third author wants also to express her gratitude to Universidad Nacional Autónoma de México for the financial support during her postdoc
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Balbuena, C., Galeana-Sánchez, H. & Guevara, Mk. A sufficient condition for kernel perfectness of a digraph in terms of semikernels modulo F . Acta. Math. Sin.-English Ser. 28, 349–356 (2012). https://doi.org/10.1007/s10114-012-9754-6
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DOI: https://doi.org/10.1007/s10114-012-9754-6