The Price of Connectivity for Vertex Cover

نویسندگان

Eglantine Camby

Jean Cardinal

Samuel Fiorini

Oliver Schaudt

چکیده

Connected vertex covers are found in many applications, and the relationship between those two graph invariants is therefore a natural question to investigate. For that purpose, we introduce the Price of Connectivity, defined as the ratio between the two vertex cover numbers. We prove that the price of connectivity is at most 2 for arbitrary graphs. We further consider graph classes in which the price of connectivity of every induced subgraph is bounded by some real number t. We obtain forbidden induced subgraph characterizations for every real value t ≤ 3/2.

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