  A Meyniel graph is a graph in which every odd cycle of length at least five
has two chords. In the manuscript "Coloring Meyniel graphs in linear time" we
claimed that our algorithm MCColor produces an optimal coloring for every
Meyniel graph. But later we found a mistake in the proof and a couterexample to
the optimality, which we present here. MCColor can still be used to find a
stable set that intersects all maximal cliques of a Meyniel graph in linear
time. Consequently it can be used to find an optimal coloring in time O(nm),
and the same holds for Algorithm MCS+Color. This is explained in the manuscript
"A linear algorithm to find a strong stable set in a Meyniel graph" but this is
equivalent to Hertz's algorithm. The current best algorithm for coloring
Meyniel graphs is the O(n^2) algorithm LexColor due to Roussel and Rusu. The
question of finding a linear-time algorithm to color Meyniel graphs is still
open.
