Decompositions of complete multigraphs into cycles of varying lengths
Darryn Bryant, Daniel Horsley, Barbara Maenhaut, Benjamin R. Smith
TL;DR
This paper provides a comprehensive characterization of when complete multigraphs can be decomposed into cycles of specified lengths, including cases with additional perfect matchings, advancing the understanding of graph decompositions.
Contribution
It establishes necessary and sufficient conditions for decomposing complete multigraphs into cycles of given lengths, including cases with perfect matchings.
Findings
Derived conditions for cycle decompositions in complete multigraphs
Extended results to include decompositions with perfect matchings
Provided a complete characterization for such decompositions
Abstract
We establish necessary and sufficient conditions for the existence of a decomposition of a complete multigraph into edge-disjoint cycles of specified lengths, or into edge-disjoint cycles of specified lengths and a perfect matching.
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.