1,742 research outputs found
Minimum Number of k-Cliques in Graphs with Bounded Independence Number
Erdos asked in 1962 about the value of f(n,k,l), the minimum number of
k-cliques in a graph of order n and independence number less than l. The case
(k,l)=(3,3) was solved by Lorden. Here we solve the problem (for all large n)
when (k,l) is (3,4), (3,5), (3,6), (3,7), (4,3), (5,3), (6,3), and (7,3).
Independently, Das, Huang, Ma, Naves, and Sudakov did the cases (k,l)=(3,4) and
(4,3).Comment: 25 pages. v4: Three new solved cases added: (3,5), (3,6), (3,7). All
calculations are done with Version 2.0 of Flagmatic no
The history of degenerate (bipartite) extremal graph problems
This paper is a survey on Extremal Graph Theory, primarily focusing on the
case when one of the excluded graphs is bipartite. On one hand we give an
introduction to this field and also describe many important results, methods,
problems, and constructions.Comment: 97 pages, 11 figures, many problems. This is the preliminary version
of our survey presented in Erdos 100. In this version 2 only a citation was
complete
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