Chromatic number, girth and maximal degree


It is proved that for every k≥4 there is a Δ(k) such that for every g there is a graph G with maximal degree at most Δ(k), chromatic number at least k and girth at least g. In fact, for a fixed k, the restriction of the maximal degree to Δ(k) does not seem to slow down the growth of the maximal girth of a k-chromatic graph of order n as n → ∞. © 1978.

Publication Title

Discrete Mathematics