The reduction of graph families closed under contraction

Abstract Let S be a family of graphs. Suppose there is a nontrivial graph H such that for any supergraph G of H , G is in S if and only if the contraction G / H is in S . Examples of such an S : graphs with a spanning closed trail; graphs with at least k edge-disjoint spanning trees; and k -edge-connected graphs ( k fixed). We give a reduction method using contractions to find when a given graph is in S and to study its structure if it is not in S . This reduction method generalizes known special cases.

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