Open packing number for some classes of perfect graphs. (English) Zbl 1462.05154

Summary: Let \(G\) be a graph with the vertex set \(V(G)\). A subset \(S\) of \(V(G)\) is an open packing set of \(G\) if every pair of vertices in \(S\) has no common neighbor in \(G\). The maximum cardinality of an open packing set of \(G\) is the open packing number of \(G\) and it is denoted by \(\rho^o(G)\). In this paper, the exact values of the open packing numbers for some classes of perfect graphs, such as split graphs, \(\{P_4, C_4\} \)-free graphs, the complement of a bipartite graph, the trestled graph of a perfect graph are obtained.


05C17 Perfect graphs
05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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