On a conjecture of Gallai concerning complete subgraphs of k-critical graphs

@article{Abbott1992OnAC,
title={On a conjecture of Gallai concerning complete subgraphs of k-critical graphs},
author={H. L. Abbott and Bing Zhou},
journal={Discrete Mathematics},
year={1992},
volume={100},
pages={223-228}
}

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-critical graph of order n contains at most n complete subgraphs of order k 1. This is clearly so when k = n, and it is also true when k = 3 since the only 3-critical graphs are the cycles of odd length. M… CONTINUE READING