Edge Contraction and Line Graphs
Abstract
Given a family of graphs H, a graph G is H-free if any subset of V(G) does not induce a subgraph of G that is isomorphic to any graph in H. We present sufficient and necessary conditions for a graph G such that G/e is H-free for any edge e in E(G). Thereafter, we use these conditions to characterize claw-free and line graphs.
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