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- W2041133760 abstract "Using a clever inductive counting argument Erdős, Kleitman and Rothschild showed in 1976 that almost all triangle-free graphs are bipartite, i.e., that the cardinality of the two graph classes is asymptotically equal. In this paper we investigate the structure of the “few” triangle-free graphs which are not bipartite. As it turns out, with high probability, these graphs are bipartite up to a few vertices. More precisely, almost all of them can be made bipartite by removing just one vertex. Almost all others can be made bipartite by removing two vertices, and then three vertices and so on. We also show that similar results hold if we replace “triangle-free” by K𝓁+1-free and “bipartite” by 𝓁-partite. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 19, 37–53, 2001" @default.
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- W2041133760 date "2001-07-20" @default.
- W2041133760 modified "2023-09-27" @default.
- W2041133760 title "On the structure of clique-free graphs" @default.
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- W2041133760 doi "https://doi.org/10.1002/rsa.1017" @default.
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