Some advances on Sidorenko's conjecture

Author: 

Conlon, D
Kim, J
Lee, C
Lee, J

Publication Date: 

December 2018

Journal: 

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES

Last Updated: 

2019-09-13T13:06:34.563+01:00

Issue: 

3

Volume: 

98

DOI: 

10.1112/jlms.12142

page: 

593-608

abstract: 

© 2018 London Mathematical Society A bipartite graph H is said to have Sidorenko's property if the probability that the uniform random mapping from V (H) to the vertex set of any graph G is a homomorphism is at least the product over all edges in H of the probability that the edge is mapped to an edge of G. In this paper, we provide three distinct families of bipartite graphs that have Sidorenko's property. First, using branching random walks, we develop an embedding algorithm which allows us to prove that bipartite graphs admitting a certain type of tree decomposition have Sidorenko's property. Second, we use the concept of locally dense graphs to prove that subdivisions of certain graphs, including cliques, have Sidorenko's property. Third, we prove that if H has Sidorenko's property, then the Cartesian product of H with an even cycle also has Sidorenko's property.

Symplectic id: 

854382

Download URL: 

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article