The Heawood graph and the complete bipartite graph $K_{3,3}$ have the property that all of their 2-factors are hamiltonian cycles. We call such graphs 2-factor hamiltonian. In this paper, we study k-regular bipartite graphs with the apparently more general property that all their 2-factors are isomorphic. We prove that if G is a k-regular bipartite graph and all 2-factors of G are isomorphic then $k \le 3$.
Regular bipartite graphs with all 2-factors isomorphic
FUNK, Martin;LABBATE, Domenico;
2004-01-01
Abstract
The Heawood graph and the complete bipartite graph $K_{3,3}$ have the property that all of their 2-factors are hamiltonian cycles. We call such graphs 2-factor hamiltonian. In this paper, we study k-regular bipartite graphs with the apparently more general property that all their 2-factors are isomorphic. We prove that if G is a k-regular bipartite graph and all 2-factors of G are isomorphic then $k \le 3$.File in questo prodotto:
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