Highly edge-connected regular graphs without large factorizable subgraphs
Davide Mattiolo, Eckhard Steffen
TL;DR
This paper constructs highly edge-connected regular graphs lacking large factorizable subgraphs, addressing a question about the structure of such graphs and their perfect matchings.
Contribution
It provides explicit constructions of highly edge-connected regular graphs without certain large factorizable subgraphs, advancing understanding of graph factorization properties.
Findings
Constructed regular graphs with high edge-connectivity
Graphs lack $r-2$ disjoint perfect matchings
Partially answers Thomassen's open question
Abstract
We construct highly edge-connected -regular graph which do not contain pairwise disjoint perfect matchings. The results partially answer a question stated by Thomassen [Factorizing regular graphs, J. Comb. Theory Ser. B (2019), https://doi.org/10.1016/j.jctb.2019.05.002 (article in press)].
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.