Editing Meyniel graph (section)

==Perfection==
The Meyniel graphs are a subclass of the perfect graphs. Every [[induced subgraph]] of a Meyniel graph is another Meyniel graph, and in every Meyniel graph the size of a [[maximum clique]] equals the minimum number of colors needed in a [[graph coloring]]. Thus, the Meyniel graphs meet the definition of being a perfect graph, that the clique number equals the chromatic number in every induced subgraph.<ref name="isgci"/><ref name="m76"/><ref name="mk"/>

Meyniel graphs are also called the '''very strongly perfect graphs''', because (as Meyniel conjectured and Hoàng proved) they can be characterized by a property generalizing the defining property of the [[strongly perfect graph]]s: in every induced subgraph of a Meyniel graph, every vertex belongs to an [[independent set (graph theory)|independent set]] that intersects every [[maximal clique]].<ref name="isgci"/><ref>{{citation
 | last = Hoàng | first = C. T.
 | doi = 10.1016/0095-8956(87)90047-5
 | issue = 3
 | journal = [[Journal of Combinatorial Theory]]
 | mr = 888682
 | pages = 302–312
 | series = Series B
 | title = On a conjecture of Meyniel
 | volume = 42
 | year = 1987| doi-access = free
 }}.</ref>