Marc's conjecture on vertex-transitive partial cubes of girth 6
Let be a vertex-transitive partial cube with girth . Marc's conjecture. Doubled Odd graphs are the only vertex-transitive partial cubes with girth . This conjecture proposes that the known Doubled Odd graphs exhaust the vertex-transitive partial cubes of girth ; its resolution is not established in the supplied text.
References
Primary source
Yan-Ting Xie, Yong-De Feng and Shou-Jun Xu, “A characterization of regular partial cubes whose all convex cycles have the same lengths”, arXiv:2301.12200 (2024).
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