---
res:
bibo_abstract:
- "Thomassen [Problem 1 in Factorizing regular graphs, J. Combin. Theory Ser. B,
141 (2020), 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 if r≡2 mod 4. Together with a recent result of Mattiolo and Steffen [Highly
edge-connected regular graphs without large factorizable subgraphs, J. Graph Theory,
99 (2022), 107-116] this solves Thomassen's problem for all even r.\r\nIt turns
out that our methods are limited to the even case of Thomassen's problem. We then
prove some equivalences of statements on pairwise disjoint perfect matchings in
highly edge-connected regular graphs, where the perfect matchings contain or avoid
fixed sets of edges.\r\nBased on these results we relate statements on pairwise
disjoint perfect matchings of 5-edge-connected 5-regular graphs to well-known
conjectures for cubic graphs, such as the Fan-Raspaud Conjecture, the Berge-Fulkerson
Conjecture and the 5-Cycle Double Cover Conjecture. @eng"
bibo_authorlist:
- foaf_Person:
foaf_givenName: Yulai
foaf_name: Ma, Yulai
foaf_surname: Ma
- foaf_Person:
foaf_givenName: Davide
foaf_name: Mattiolo, Davide
foaf_surname: Mattiolo
- foaf_Person:
foaf_givenName: Eckhard
foaf_name: Steffen, Eckhard
foaf_surname: Steffen
foaf_workInfoHomepage: http://www.librecat.org/personId=15548
- foaf_Person:
foaf_givenName: Isaak Hieronymus
foaf_name: Wolf, Isaak Hieronymus
foaf_surname: Wolf
foaf_workInfoHomepage: http://www.librecat.org/personId=88145
dct_date: 2022^xs_gYear
dct_language: eng
dct_title: Pairwise disjoint perfect matchings in r-edge-connected r-regular graphs@
...