A characterisation of Pfaffian near bipartite graphs

Details A characterisation of Pfaffian near bipartite graphs A characterisation of Pfaffian near bipartite graphs

2000-02-09

arxiv.org/abs/math/0002062v1

Mathematics

Combinatorics

Scientific paper

In 1967 Kasteleyn introduced a powerful method for enumerating the 1-factors of planar graphs. In fact his method can be extended to graphs which permit an orientation under which every alternating circuit is clockwise odd. Graphs with this property are called {\it Pfaffian}. Little characterised Pfaffian bipartite graphs in terms of forbidden subgraphs in 1975. We extend his characterisation to near bipartite graphs.

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