Abstract.
Moving from a well known result of Hammer, Hansen, and Simeone, we introduce a new graph invariant, say λ(G) referring to any graph G. It is a non-negative integer which is non-zero whenever G contains particular induced odd cycles or, equivalently, admits a particular minimum clique-partition. We show that λ(G) can be efficiently evaluated and that its determination allows one to reduce the hard problem of computing a minimum clique-cover of a graph to an identical problem of smaller size and special structure. Furthermore, one has α(G)≤θ(G)−λ(G), where α(G) and θ(G) respectively denote the cardinality of a maximum stable set of G and of a minimum clique-partition of G.
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Received: April 12, 1999 Final version received: September 15, 2000
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Mosca, R. A Shy Invariant of Graphs. Graphs Comb 18, 367–379 (2002). https://doi.org/10.1007/s003730200027
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DOI: https://doi.org/10.1007/s003730200027