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Meyniel graph
Graph where all odd cycles of length ≥ 5 has 2+ chords / From Wikipedia, the free encyclopedia
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In graph theory, a Meyniel graph is a graph in which every odd cycle of length five or more has at least two chords (edges connecting non-consecutive vertices of the cycle).[1] The chords may be uncrossed (as shown in the figure) or they may cross each other, as long as there are at least two of them.
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The Meyniel graphs are named after Henri Meyniel (also known for Meyniel's conjecture), who proved that they are perfect graphs in 1976,[2] long before the proof of the strong perfect graph theorem completely characterized the perfect graphs. The same result was independently discovered by Markosjan & Karapetjan (1976).[3]