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- W2005131446 abstract "A graph is clique-perfect if the maximum size of a clique-independent set (a set of pairwise disjoint maximal cliques) and the minimum size of a clique-transversal set (a set of vertices meeting every maximal clique) coincide for each induced subgraph. A graph is balanced if its clique-matrix contains no square submatrix of odd size with exactly two ones per row and column. In this work, we give linear-time recognition algorithms and minimal forbidden induced subgraph characterizations of clique-perfectness and balancedness of P4-tidy graphs and a linear-time algorithm for computing a maximum clique-independent set and a minimum clique-transversal set for any P4-tidy graph. We also give a minimal forbidden induced subgraph characterization and a linear-time recognition algorithm for balancedness of paw-free graphs. Finally, we show that clique-perfectness of diamond-free graphs can be decided in polynomial time by showing that a diamond-free graph is clique-perfect if and only if it is balanced." @default.
- W2005131446 created "2016-06-24" @default.
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- W2005131446 date "2014-03-26" @default.
- W2005131446 modified "2023-10-09" @default.
- W2005131446 title "Clique-perfectness and balancedness of some graph classes" @default.
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- W2005131446 doi "https://doi.org/10.1080/00207160.2014.881994" @default.
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