Abstract
An even pair in a graph is a pair of vertices such that every chordless path between them has even length. A graph is called perfectly contractile when every induced subgraph can be transformed into a clique through a sequence of even-pair contractions. In this paper we characterize the planar graphs that are perfectly contractile by determining all the minimal forbidden subgraphs. We give a polynomial algorithm for the recognition of perfectly contractile planar graphs.
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Sales, C.L., Maffray, F. & Reed, B. On Planar Perfectly Contractile Graphs. Graphs and Combinatorics 13, 167–187 (1997). https://doi.org/10.1007/BF03352994
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DOI: https://doi.org/10.1007/BF03352994