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A 2-matching in an undirected graph G = (V G, EG) is a function x : EG → {0, 1, 2} such that for each node v ∈ V G the sum of values x(e) on all edges e incident to v does not exceed 2. The size of x is the sum e x(e). If {e ∈ EG | x(e) = 0} contains no triangles then x is called triangle-free. Cornuéjols and Pulleyblank devised a combinatorial… (More)

By a T-star we mean a complete bipartite graph K 1,t for some t ≤ T. For an undirected graph G, a T-star packing is a collection of node-disjoint T-stars in G. For example, we get ordinary matchings for T = 1 and packings of paths of length 1 and 2 for T = 2. Hereinafter we assume that T ≥ 2. Hell and Kirkpatrick devised an ad-hoc augmenting algorithm that… (More)

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