Mathematical Programming: Series A and B
Discrete Mathematics - Special issue: selected papers in honour of Paul Erdo&huml;s on the occasion of his 80th birthday
Notes: Markov bases of binary graph models of K4-minor free graphs
Journal of Combinatorial Theory Series A
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An integral convex polytope P is said to be Gorenstein if its toric ring K[P] is normal and Gorenstein. In this paper, Gorenstein cut polytopes of graphs are characterized explicitly. First, we prove that Gorenstein cut polytopes are compressed (i.e., all of whose reverse lexicographic triangulations are unimodular). Second, by applying Athanasiadis's theory for Gorenstein compressed polytopes, we show that a cut polytope of a graph G is Gorenstein if and only if G has no K"5-minor and G is either a bipartite graph without induced cycles of length =6 or a bridgeless chordal graph.