Counterexamples to the Kneser conjecture in dimension four
✍ Scribed by Matthias Kreck; Wolfgang Lück; Peter Teichner
- Book ID
- 110557942
- Publisher
- European Mathematical Society
- Year
- 1995
- Tongue
- English
- Weight
- 511 KB
- Volume
- 70
- Category
- Article
- ISSN
- 0010-2571
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
A pair of vertices (x, y) of a graph G is an ω-critical pair if ω(G + xy) > ω(G), where G + xy denotes the graph obtained by adding the edge xy to G and ω(H) is the clique number of H. The ω-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
It has been conjectured by C. van Nuffelen that the chromatic number of any graph with at least one edge does not exceed the rank of its adjacency matrix. We give a counterexample, with chromatic number 32 and with an adjacency matrix of rank 29.