Unions of 1-factors in $r$-graphs and overfull graphs
Combinatorics
2019-10-07 v2
Abstract
We prove lower bounds for the fraction of edges of an -graph which can be covered by the union of 1-factors. The special case yields some known results for cubic graphs. Furthermore, we introduce the concept of -overfull-free -graphs and achieve better bounds for these graphs.
Cite
@article{arxiv.1509.01823,
title = {Unions of 1-factors in $r$-graphs and overfull graphs},
author = {Ligang Jin and Eckhard Steffen},
journal= {arXiv preprint arXiv:1509.01823},
year = {2019}
}
Comments
14 pages, no figure, 1 table. To be published in Journal of Combinatorics. Difference from the previous version: We add the results on overfull graphs, stated in Chapter 4; Moreover, Corollary 3.2 is new