错误：MCColor在Meyniel图上不是最优的
Erratum : MCColor is not optimal on Meyniel graphs
摘要：
Meyniel图是一个图，其中每个长度至少为5的奇数圈都有两个弦。在手稿“着色Meyniel图在线性时间”中，我们声称我们的算法MCColor为每个Meyniel图产生最佳着色。但后来我们发现了证明中的一个错误和最优性的一个反例，我们在这里提出。MCColor仍然可以用来找到一个稳定的集，相交的所有最大团的Meyniel图在线性时间。因此，它可以用于在时间O（nm）内找到最佳着色，并且同样适用于算法MCS+Color。这是解释的手稿“一个线性算法找到一个强大的稳定集的Meyniel图”，但这是相当于赫兹的算法。目前最好的Meyniel图的着色算法是O（n^2）算法LexColor，这是由Reisel和Rusu提出的。寻找一个线性时间算法来着色Meyniel图的问题仍然是开放的。
英文摘要：
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.
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