The computational complexity of the Edge-Perfect Graph and the Totally Balanced Packing Game recognition problems (original) (raw)
2010, Electronic Notes in Discrete Mathematics
Edge-perfect graphs were introduced by Escalante et al (2009). An edge-subgraph of a given graph is an induced subgraph obtained by deletion of the endpoints of a subset of edges. A graph is edge-perfect if the stability and the edge covering numbers coincide for every edge-subgraph. In this work we prove that the recognition of edge-perfect graphs is an NP-hard problem. As a by-product, we derive the NP-completeness of two related problems in graphs. From the NP-hardness of the edge-perfection recognition problem we answer the open question on the recognition of totally balanced packing game defining matrices-raised by Deng et al. in 2000-, obtaining that this problem is NP-hard in contrast with the polynomiality for the covering case due to van Velzen (2005).
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