The reduction of graph families closed under contraction Original Research Article

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.