Let D b a k-connected digraph with independence number (Y. We show that for any integers t and p such that k 3 $ti (t + 1) i-p, then any set of arcs of cardinal@ p inducing a subgraph with maximum in-and outdegree at most t is contained in a spanning subgraph which is regular of in-and out-degree t,
A Chvátal-Erdös condition for (1,1)-factors in digraphs
✍ Scribed by Bill Jackson; Oscat Ordaz
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 171 KB
- Volume
- 57
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
We show that if the independence number of a k-connected digraph D is at most k, then D has a spanning subgraph which consists of a union of vertex-disjoint directed circuits. As a corollary we determine the minimum number of edges required in a k-connected oriented graph to ensure the existence of such a subgraph.
📜 SIMILAR VOLUMES
## Abstract Chvátal and Erdös showed that a __k__‐connected graph with independence number at most __k__ and order at least three is hamiltonian. In this paper, we show that a graph contains a 2‐factor with two components, i.e., the graph can be divided into two cycles if the graph is __k__(≥ 4)‐co
We give a survey of results and conjectures concerning sufficient conditions in terms of connectivity and independence number for which a graph or digraph has various path or cyclic properties, for example hamilton path/cycle, hamilton connected, pancyclic, path/cycle covers, 2-cyclic.
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