An O(n2) algorithm to color Meyniel graphs Original Research Article

Meyniel graphs are the graphs in which every odd cycle with five vertices or more has at least two chords. In 1990, Hertz gave an O(mn) algorithm to color Meyniel graphs based on successive contractions of even pairs. We give here another algorithm which consists in simultaneously ordering (in a Lex-BFS way) and coloring (with the greedy algorithm) the vertices of the graph and we show that it needs only O(n2) operations.