Tutte's edge-coloring conjecture
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Disconnected 2-factors in planar cubic bridgeless graphs
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
Regular bipartite graphs with all 2-factors isomorphic
Journal of Combinatorial Theory Series B
Graphs and digraphs with all 2-factors isomorphic
Journal of Combinatorial Theory Series B - Special issue dedicated to professor W. T. Tutte
Pseudo 2-factor isomorphic regular bipartite graphs
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series B
European Journal of Combinatorics
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A graph G is pseudo 2-factor isomorphic if the parity of the number of cycles in a 2-factor is the same for all 2-factors of G. In Abreu et al. (2008) [3] we proved that pseudo 2-factor isomorphic k-regular bipartite graphs exist only for k@?3. In this paper we generalize this result for regular graphs which are not necessarily bipartite. We also introduce strongly pseudo 2-factor isomorphic graphs and we prove that pseudo and strongly pseudo 2-factor isomorphic 2k-regular graphs and k-regular digraphs do not exist for k=4. Moreover, we present constructions of infinite families of regular graphs in these classes. In particular we show that the family of Flower snarks is strongly pseudo 2-factor isomorphic but not 2-factor isomorphic and we conjecture that, together with the Petersen and the Blanusa2 graphs, they are the only cyclically 4-edge-connected snarks for which each 2-factor contains only cycles of odd length.