## 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
Counterexamples to Q-matrix conjectures
β Scribed by Walter D. Morris Jr.
- Publisher
- Elsevier Science
- Year
- 1988
- Tongue
- English
- Weight
- 564 KB
- Volume
- 111
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We give a polynomial counterexample to a discrete version of the MarkusαYamabe conjecture and a conjecture of Deng, Meisters, and Zampieri, Ε½ . asserting that if F: β«ήβ¬ Βͺ β«ήβ¬ is a polynomial map with det JF g β«,\*ήβ¬ then for all g β«ήβ¬ large enough, F is global analytic linearizable. These counterex
We will present counterexamples to a conjecture of Hoang on alternately orientable graphs, a conjecture of Hertz and de Werra on even pairs and to a conjecture of Reed on Berge graphs. All these three conjectures are related to perfect graphs.
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