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Minimum number of k-Cliques in graphs with bounded independence number
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Pikhurko, Oleg and Vaughan, Emil (2013) Minimum number of k-Cliques in graphs with bounded independence number. Combinatorics, Probability and Computing, Volume 22 (Number 6). pp. 910-934. doi:10.1017/S0963548313000357
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Official URL: http://dx.doi.org/10.1017/S0963548313000357
Abstract
Erdős asked in 1962 about the value of f(n,k,l), the minimum number of k-cliques in a graph with 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) for (3,l) with 4 ≤ l ≤ 7 and (k,3) with 4 ≤ k ≤ 7. Independently, Das, Huang, Ma, Naves and Sudakov resolved the cases (k,l)=(3,4) and (4,3).
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Divisions: | Faculty of Science > Mathematics | ||||||
| Journal or Publication Title: | Combinatorics, Probability and Computing | ||||||
| Publisher: | Cambridge University Press | ||||||
| ISSN: | 0963-5483 | ||||||
| Official Date: | November 2013 | ||||||
| Dates: |
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| Volume: | Volume 22 | ||||||
| Number: | Number 6 | ||||||
| Page Range: | pp. 910-934 | ||||||
| DOI: | 10.1017/S0963548313000357 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Restricted or Subscription Access |
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