Acyclic edge coloring of sparse graphs
An acyclic edge coloring of a graph \(G\) is a proper edge coloring that results in no bichromatic cycle. A graph \(G\) ist called acyclically edge \(k\)-colorable if it admits an acyclic edge coloring using at most \(k\) colours. The acyclic chromatic index of a graph \(G\) is the minimum number \(k\) such that \(G\) is acyclically edge \(k\)-colorable. In 1978 it was conjectured that every graph is acyclically edge \((\Delta+2)\)-colorable. In the present paper the conjecture is proved for graphs with maximum average degree less than 4. As a corollary, triangle-free planar graphs prove to be edge \((\Delta+2)\)-colorable.
scientific article; zbMATH DE number 6108949