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Acyclic coloring of graphs. (English) Zbl 0735.05036
A proper vertex colouring (adjacent vertices have distinct colours) of a finite simple undirected graph \(G\) is acyclic if there is no cycle in \(G\) induced by the vertices of any two of the colours. The acyclic chromatic number \(A(G)\) of \(G\) is the least number of colours in an acyclic colouring of \(G\). The main result \[ A(G)=O(d^{4/3}) \hbox{ as } d\to \infty \] for every graph \(G\) of maximum degree \(d\) settles a problem of Erdős. All proofs rely heavily on probabilistic arguments.
Reviewer: U.Baumann

MSC:
05C15 Coloring of graphs and hypergraphs
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