Bipartizing matchings and Sabidussi's compatibility conjecture

Authors:
Herbert Fleischner
Affiliations:
Institute for Discrete Mathematics, Austrian Academy of Sciences, Sonnenfelsgasse 19, A-1010 Vienna, Austria
Venue:
Discrete Mathematics - Algebraic and topological methods in graph theory
Year:
2002

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Abstract

In a cubic graph G3 with dominating cycle C, a matching M is called bipartizing if M ∩ E(C) = φ, M covers all of V(G3)- V(C), and G3 - M is homeomorphic to a cubic bipartite graph. In this note it will be shown that if G3 has two disjoint bipartizing matchings, then G3 has a cycle double cover S with C ∈ S.