The hardness of recognising poorly matchable graphs and the hunting of the d-snark
Leandro M. Zatesko,
Renato Carmo,
André L.P. Guedes
et al.
Abstract:Abstract. An r-graph is an r-regular graph G on an even number of vertices where every odd set X ⊆V(G) is connected by at least r edges to its complement V(G) \ X. Every r-graph has a perfect matching and in a poorly matchable r-graph every pair of perfect matchings intersect, which implies that poorly matchable r-graphs are not r-edge-colourable. We prove, for each fixed r ≥ 3, that poorly matchable r-graph recognition is coNP-complete, an indication that, for each odd d ≥ 3, it may be a hard problem to recog… Show more
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