Abstract
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 → ∞.
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