On a conjecture of Murty and Simon on diameter two critical graphs II
β Scribed by Teresa W. Haynes; Michael A. Henning; Anders Yeo
- Book ID
- 113567457
- Publisher
- Elsevier Science
- Year
- 2012
- Tongue
- English
- Weight
- 250 KB
- Volume
- 312
- Category
- Article
- ISSN
- 0012-365X
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## Abstract Mader conjectured that every __k__βcritical __n__βconnected noncomplete graph __G__ has __2k__β+β2 pairwise disjoint fragments. The author in 9 proved that the conjecture holds if the order of __G__ is greater than (__k__β+β2)__n__. Now we settle this conjecture completely. Β© 2004 Wiley
Abbott, H.L. and B. Zhou, On a conjecture of Gallai concerning complete subgraphs of k-critical graphs, Discrete Mathematics 100 (1992) 223-228. A graph G is said to be k-critical if it has chromatic number k but every proper subgraph of G has a (k -l)-coloring. T. Gallai asked whether each k-criti