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One-Three Join: A Graph Operation and Its Consequences

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Shalu M. A., Devi Yamini S.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 3

633-647

In this paper, we introduce a graph operation, namely one-three join. We show that the graph G admits a one-three join if and only if either G is one of the basic graphs (bipartite, complement of bipartite, split graph) or G admits a constrained homogeneous set or a bipartite-join or a join. Next, we define ℳH as the class of all graphs generated from the induced subgraphs of an odd hole-free graph H that contains an odd anti-hole as an induced subgraph by using one-three join and co-join recursively and show that the maximum independent set problem, the maximum clique problem, the minimum coloring problem, and the minimum clique cover problem can be solved efficiently for ℳH.

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1 Discussiones Mathematicae Graph Theory

1 Devi Yamini S.

1 Shalu M. A.

1 2017

Wyniki wyszukiwania

One-Three Join: A Graph Operation and Its Consequences