论文信息 - Pseudo 2-factor isomorphic regular bipartite graphs

Pseudo 2-factor isomorphic regular bipartite graphs

A graph G is pseudo 2-factor isomorphic if the parity of the number of circuits in a 2-factor is the same for all 2-factors of G. We prove that there exist no pseudo 2-factor isomorphic k-regular bipartite graphs for k>=4. We also propose a characterization for 3-edge-connected pseudo 2-factor isomorphic cubic bipartite graphs and obtain some partial results towards our conjecture.

Bill Jackson | John Sheehan | Domenico Labbate | Marién Abreu | A. A. Diwan

[1] William McCuaig. Even dicycles , 2000 .

[2] Carsten Thomassen. The even cycle problem for directed graphs , 1992 .

[3] Carsten Thomassen,et al. The Even Cycle Problem for Planar Digraphs , 1993, J. Algorithms.

[4] D. Frank Hsu,et al. Graph Theory, Combinatorics, Algorithms, and Applications , 1991 .

[5] Armen S. Asratian. Short Solution of Kotzig's Problem for Bipartite Graphs , 1998, J. Comb. Theory, Ser. B.

[6] Ajit A. Diwan. Disconnected 2-Factors in Planar Cubic Bridgeless Graphs , 2002, J. Comb. Theory, Ser. B.

[7] Michael D. Plummer,et al. Two results on matching extensions with prescribed and proscribed edge sets , 1999, Discret. Math..

[8] N. Biggs. Algebraic Graph Theory , 1974 .

[9] Michael S. Jacobson,et al. On the Extremal Number of Edges in 2-Factor Hamiltonian Graphs , 2006 .

[10] Bill Jackson,et al. Regular bipartite graphs with all 2-factors isomorphic , 2004, J. Comb. Theory, Ser. B.

[11] Bill Jackson,et al. 2-Factor hamiltonian graphs , 2003, J. Comb. Theory, Ser. B.

[12] Michael D. Plummer,et al. On matching extensions with prescribed and proscribed edge sets II , 1999 .

[13] Gordon F. Royle,et al. Algebraic Graph Theory , 2001, Graduate texts in mathematics.