Towards a characterisation of Pfaffian graphs

Details Towards a characterisation of Pfaffian graphs Towards a characterisation of Pfaffian graphs

1999-09-03

arxiv.org/abs/math/9909026v2

Mathematics

Combinatorics

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Scientific paper

A bipartite graph G is known to be Pfaffian if and only if it does not contain an even subdivision H of $K_{3,3}$ such that $G - VH$ contains a 1-factor. However a general characterisation of Pfaffian graphs in terms of forbidden subgraphs is currently not known. In this paper we describe a possible approach to the derivation of such a characterisation. We also extend the characterisation for bipartite graphs to a slightly more general class of graphs.

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