Abstract
Motivated by the identity t (K n+2; 1, –1) = t (K n ; 2, –1), where t(G; x, y) is the Tutte polynomial of a graph G, we search for graphs G having the property that there is a pair of vertices u, v such that t(G; 1, –1) = t(G – {u, v}; 2, –1). Our main result gives a sufficient condition for a graph to have this property; moreover, it describes the graphs for which the property still holds when each vertex is replaced by a clique or a coclique of arbitrary order. In particular, we show that the property holds for the class of threshold graphs, a well-studied class of perfect graphs.
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Supported by ITI 1M0545.
Investigación realizada gracias al Programa UNAM-DGAPA-PAPIIT IN100312-2.
Partially supported by Projects MTM2011-24097 and Gen. Cat. DGR 2009SGR1040.
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Goodall, A.J., Merino, C., de Mier, A. et al. On the Evaluation of the Tutte Polynomial at the Points (1, –1) and (2, –1). Ann. Comb. 17, 311–332 (2013). https://doi.org/10.1007/s00026-013-0180-y
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DOI: https://doi.org/10.1007/s00026-013-0180-y