Cliques and clustering: A combinatorial approach
Operations Research Letters
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The graph partitioning polytope $P(G)$ is the convex hull of the incidence vectors of all partitions of a graph $G$. The authors show that $P(G)$ is completely defined by cycle inequalities if $G$ is series- parallel and by cycle, 3-wheel, and repeated 2-sums of 3-wheel and cycle inequalities if $G$ is a 4-wheel free graph.