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Graphs without odd holes, parachutes or proper wheels: A generalization of Meyniel graphs and of line graphs of bipartite graphs. (English) Zbl 1030.05049
A hole is a cordless cycle of length at least four. A hole is odd if it has an odd number of vertices. The strong perfect graph conjecture states that a graph $$G$$ is perfect if neither $$G$$ nor $$\overline G$$ has an odd hole. The authors prove the conjecture for graphs that do not contain parachutes and proper wheels. Recently, M. Chudnovsky, N. Robertson, P. D. Seymoud and R. Thomas [Math. Program. 97B, 405-422 (2002; Zbl 1028.05035)] proved the conjecture for all graphs.

##### MSC:
 05C17 Perfect graphs 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.)
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##### References:
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