Lee, J;
(2021)
On some graph densities in locally dense graphs.
Random Structures & Algorithms
, 58
(2)
pp. 322-344.
10.1002/rsa.20974.
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Abstract
The Kohayakawa–Nagle–Rödl‐Schacht conjecture roughly states that every sufficiently large locally d‐dense graph G on n vertices must contain at least (1 − o(1))d|E(H )|n|V (H )| copies of a fixed graph H. Despite its important connections to both quasirandomness and Ramsey theory, there are very few examples known to satisfy the conjecture. We provide various new classes of graphs that satisfy the conjecture. First, we prove that adding an edge to a cycle or a tree produces graphs that satisfy the conjecture. Second, we prove that a class of graphs obtained by gluing complete multipartite graphs in a tree‐like way satisfies the conjecture. We also prove an analogous result with odd cycles replacing complete multipartite graphs.
| Type: | Article |
|---|---|
| Title: | On some graph densities in locally dense graphs |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1002/rsa.20974 |
| Publisher version: | http://dx.doi.org/10.1002/rsa.20974 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Software Engineering, Mathematics, Applied, Mathematics, Computer Science, graph inequalities, quasirandomness, Ramsey theory |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10120250 |
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