Lawrence [2, Theorem 3] and Borodin and Kostochka [1, Lemma 2' 1 both give the same theorem about vertex colorings of graphs (Corollary 1 below). But Lawrence's proof, although powerful, is a little long, and Borodin and Kostoehka state the result without a proof.
Vertex maps on graphs-trace theorems
โ Scribed by Chris Bernhardt
- Book ID
- 115021629
- Publisher
- Springer International Publishing AG
- Year
- 2011
- Tongue
- English
- Weight
- 278 KB
- Volume
- 2011
- Category
- Article
- ISSN
- 1687-1820
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
In this note we point out a flaw in the separator theorem for rooted directed vertex graphs due to C. L. Monma and V. K. Wei (1986, J. Combin. Theory Ser. B 41, 141 181), and present a modified separator theorem for the same class of graphs.
In this paper w e determine the circumstances under which a set of 11 vertices in a 3-connected cubic graph lies on a cycle. In addition, w e consider the number of such cycles that exist and characterize those graphs in which a set of 9 vertices lies in exactly two cycles.
## Dedicated to E. Corominas Given a graph G =(X, E), we try to know when it is possible to consider G as the intersection graph of a finite hypergraph, when some restrietions are given on the inclusion order induced on the edge set of this hypergraph. We give some examples concerning the interva