Counterexamples to Robertson's conjecture
β Scribed by F.W Steutel
- Publisher
- Elsevier Science
- Year
- 1991
- Tongue
- English
- Weight
- 184 KB
- Volume
- 158
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract A simple graph **__H__** is a cover of a graph **__G__** if there exists a mapping Ο from **__H__** onto **__G__** such that Ο maps the neighbors of every vertex Ο in **__H__** bijectively to the neighbors of Ο (Ο ) in **__G__**. Negami conjectured in 1986 that a connected graph has a fi
A pair of vertices (x, y) of a graph G is an Ο-critical pair if Ο(G + xy) > Ο(G), where G + xy denotes the graph obtained by adding the edge xy to G and Ο(H) is the clique number of H. The Ο-critical pairs are never edges in G. A maximal stable set S of G is called a forced color class of G if S mee
## Abstract Counterexamples are presented to the following two conjectures of Hilton: A graph which does not contain a spanning __K__~1t~ is Vlβcritical if and only if it is VCβcritical. If __G__ is a classβtwo graph which contains a spanning Plβcritical subgraph __H__ of the same chromatic index