A semidefinite programming approach to a cross-intersection problem with measures
Combinatorics
2018-09-18 v3
Abstract
We present a semidefinite programming approach to bound the measures of cross-independent pairs in a bipartite graph. This can be viewed as a far-reaching extension of Hoffman's ratio bound on the independence number of a graph. As an application, we solve a problem on the maximum measures of cross-intersecting families of subsets with two different product measures, which is a generalized measure version of the Erd\H{o}s-Ko-Rado theorem for cross-intersecting families with different uniformities.
Cite
@article{arxiv.1504.00135,
title = {A semidefinite programming approach to a cross-intersection problem with measures},
author = {Sho Suda and Hajime Tanaka and Norihide Tokushige},
journal= {arXiv preprint arXiv:1504.00135},
year = {2018}
}
Comments
15 pages