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On degree sum conditions for directed path-factors with a specified number of paths
Discrete Mathematics ( IF 0.8 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.disc.2020.112114
Shuya Chiba , Eishi Mishio , Pierre Montalbano

Abstract A directed path-factor of a digraph is a spanning subdigraph consisting of a union of vertex-disjoint directed paths in the digraph. In this paper, we give the following result: If D is a digraph of order n ≥ ( 2 l − 1 ) k − 1 , and if d D + ( u ) + d D − ( v ) ≥ n − k for every two distinct vertices u and v with ( u , v ) ∉ A ( D ) , then D has a directed path-factor with exactly k directed paths of order at least l ( ≥ 2 ) . To show this theorem, we discuss the correspondence between digraphs and bipartite graphs with perfect matchings, and also consider degree conditions for the existence of long directed paths in digraphs.

中文翻译:

关于具有指定路径数的有向路径因子的度和条件

摘要 有向图的有向路径因子是由有向图中顶点不相交的有向路径的并集组成的生成子有向图。在本文中,我们给出以下结果: 如果 D 是 n ≥ ( 2 l − 1 ) k − 1 阶的有向图,并且如果 d D + ( u ) + d D − ( v ) ≥ n − k 对于每个两个不同的顶点 u 和 v 且 ( u , v ) ∉ A ( D ) ,则 D 有一个有向路径因子,其中有正好 k 条至少为 l ( ≥ 2 ) 阶的有向路径。为了证明这个定理,我们讨论了有向图和具有完美匹配的二部图之间的对应关系,并考虑了有向图中长有向路径存在的度条件。
更新日期:2020-12-01
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