Abreu–Diwan–Jackson–Labbate–Schwenk's classification conjecture for 3-edge-connected pseudo 2-factor isomorphic graphs

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A graph is pseudo 2-factor isomorphic if all of its 2-factors have the same parity of number of cycles. A star product is the cubic graph operation that deletes one degree-3 vertex from each factor and joins the three resulting pairs of neighbours. Let GG be a 3-edge-connected cubic bipartite graph.

Abreu–Diwan–Jackson–Labbate–Schwenk's conjecture. GG is pseudo 2-factor isomorphic if and only if GG can be obtained from K3,3K_{3,3}, the Heawood graph or the Pappus graph by repeated star products.

This conjecture gives a proposed classification of all 3-edge-connected cubic bipartite graphs with the parity property. The supplied text gives no resolution of this statement.

References

Primary source

Marien Abreu, Jan Goedgebeur, Jorik Jooken, Federico Romaniello and Tibo Van den Eede, “The Gray graph is pseudo 2-factor isomorphic”, arXiv:2504.12095 (2026).

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