Journal of Combinatorics
Volume 11 (2020)
Unions of $1$-factors in $r$-graphs and overfull graphs
Pages: 457 – 473
We prove lower bounds for the fraction of edges of an $r$-graph which can be covered by the union of $k$ $1$-factors. The special case $r = 3$ yields some known results for cubic graphs. Furthermore, we introduce the concept of $k$-overfull-free $r$-graphs and achieve better bounds for these graphs.
$r$-graphs, $1$-factors, overfull graphs
The first-named author was supported by the grants NSFC 11801522 and QJD 1803023.
Received 1 September 2018
Accepted 22 July 2019
Published 11 May 2020