On the logarithimic calculus and Sidorenko's conjecture
Combinatorics
2011-07-07 v1
Abstract
We study a type of calculus for proving inequalities between subgraph densities which is based on Jensen's inequality for the logarithmic function. As a demonstration of the method we verify the conjecture of Erd\"os-Simonovits and Sidorenko for new families of graphs. In particular we give a short analytic proof for a result by Conlon, Fox and Sudakov. Using this, we prove the forcing conjecture for bipartite graphs in which one vertex is complete to the other side.
Cite
@article{arxiv.1107.1153,
title = {On the logarithimic calculus and Sidorenko's conjecture},
author = {J. L. Xiang Li and Balazs Szegedy},
journal= {arXiv preprint arXiv:1107.1153},
year = {2011}
}