Tomaž Pisanski: One factor graphs

Povzetek. The one-factor graph F(G) of a graph G is a graph with vertices consisting of one-factors in G and two vertices being adjacent if and only if the corresponding one-factors are edge-disjoint. Some properties of one-factor graphs are explored. The emphasis is on the one-factor graphs of trivalent graphs. Some other graphs, such as resonance graphs, defined on the set of one-factors of G, are mentioned.

This is work in progress with Milan Randic.