Core Index of Perfect Matching Polytope for a 2-Connected Cubic Graph
Xiumei Wang, Yixun Lin (2018)
Discussiones Mathematicae Graph Theory
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For a 2-connected cubic graph G, the perfect matching polytope P(G) of G contains a special point [...] xc=(13,13,…,13) . The core index ϕ(P(G)) of the polytope P(G) is the minimum number of vertices of P(G) whose convex hull contains xc. The Fulkerson’s conjecture asserts that every 2-connected cubic graph G has six perfect matchings such that each edge appears in exactly two of them, namely, there are six vertices of P(G) such that xc is the convex combination of them, which implies...