Seminar of Graph Theory - Davide Mattiolo (9.10.2025)
Thursday 9.10.2025 at 9:50, Lecture room M 213
Davide Mattiolo (KU Leuven, Kortrijk, Belgium):
Pairwise disjoint perfect matchings in r-edge-connected r-graphs
Abstract:
Thomassen [Factorizing regular graphs, J. Combin. Theory Ser. B 141 (2020), pp. 343–351] asked whether every r-edge-connected r-regular graph of even order has r-2 pairwise disjoint perfect matchings. We show that this is not the case when r is even.
It turns out that our methods are limited to the even case of Thomassen's problem. We discuss the odd case and relate statements on the existence of pairwise disjoint perfect matchings in 5-edge- connected 5-regular graphs to well-known conjectures on cubic graphs, such as the Fan–Raspaud conjecture, the Berge–Fulkerson conjecture, and the 5-cycle double cover conjecture.
The talk is based on joint works with Y. Ma, E. Steffen and I. H. Wolf.