Unions of $1$-factors in $r$-graphs and overfull graphs
Unions of $1$-factors in $r$-graphs and overfull graphs
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DOI：
10.4310/joc.2020.v11.n3.a2
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发表时间：
2015-09
影响因子：
0.3
通讯作者：
Li-gang Jin;E. Steffen
中科院分区：
文献类型：
--
作者：
Li-gang Jin;E. Steffen
我们证明了一个$r$-图的边的分数的下界，它可以覆盖的联合$k $1-因子。特殊情况下$r=3$产生一些已知的结果三次图。此外，我们引入了$k$-过满自由$r$-图的概念，并获得了这些图的更好的界。
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.