229 research outputs found
A bipartite graph with non-unimodal independent set sequence
We show that the independent set sequence of a bipartite graph need not be
unimodal
Mantel's Theorem for random graphs
For a graph , denote by (resp. ) the maximum size of a
triangle-free (resp. bipartite) subgraph of . Of course for
any , and a classic result of Mantel from 1907 (the first case of Tur\'an's
Theorem) says that equality holds for complete graphs. A natural question,
first considered by Babai, Simonovits and Spencer about 20 years ago is, when
(i.e. for what ) is the "Erd\H{o}s-R\'enyi" random graph
likely to satisfy ? We show that this is true if for a suitable constant , which is best possible up to the
value of .Comment: 15 page
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