On the chromatic index of path decompositions
Given a decomposition \(D\) of a graph \(H\) into edge-disjoint copies of a graph \(G\), the chromatic index of \(D\) is the minimum number of colours in any colouring of the copies of \(G\) in \(D\) in which no two copies of \(G\) having a vertex in common get the same colour. For given \(H\) and \(G\), the minimum chromatic index problem asks for the smallest chromatic index over all decompositions \(D\) of \(H\) into copies of \(G\). The authors solve this problem for the cases when \(H\) is the complete graph on \(n\) vertices, and \(G\) is the path with two and three edges, respectively.
scientific article; zbMATH DE number 2093772
scientific article