What did Ryser Conjecture?

Darcy Best; Ian M. Wanless

What did Ryser Conjecture?

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arxiv 1801.02893 v1 pith:GNYX7XSX submitted 2018-01-09 math.CO math.HO

Darcy Best , Ian M. Wanless This is my paper · ORCID

classification math.COmath.HO

keywords conjecturesnumberryserwhatattributedbeenconferenceconjecture

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Two prominent conjectures by Herbert J. Ryser have been falsely attributed to a somewhat obscure conference proceedings that he wrote in German. Here we provide a translation of that paper and try to correct the historical record at least as far as what was conjectured in it. The two conjectures relate to transversals in Latin squares of odd order and to the relationship between the covering number and the matching number of multipartite hypergraphs.

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Almost-perfect colorful matchings in three-edge-colored bipartite graphs
math.CO 2025-04 accept novelty 8.0 of 10

For any bipartite graph that is the union of three disjoint perfect matchings, a matching of size n-1 with exactly a1, a2, a3 edges from each exists whenever a1+a2+a3=n-1.

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