Approximate path decompositions of regular graphs
Abstract
We show that the edges of any $d$-regular graph can be almost decomposed into paths of length roughly $d$, giving an approximate solution to a problem of Kotzig from 1957. Along the way, we show that almost all of the vertices of a $d$-regular graph can be partitioned into $n/(d+1)$ paths, asymptotically confirming a conjecture of Magnant and Martin from 2009.
- Publication:
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arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.02514
- arXiv:
- arXiv:2406.02514
- Bibcode:
- 2024arXiv240602514M
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 34 pages, 1 figure