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 Erdős–Ko–Rado theorem for cross-intersecting families with different uniformities.
| Original language | English |
|---|---|
| Pages (from-to) | 113-130 |
| Number of pages | 18 |
| Journal | Mathematical Programming |
| Volume | 166 |
| Issue number | 1-2 |
| DOIs | |
| Publication status | Published - 2017 Nov 1 |
Keywords
- Cross-intersecting families
- Intersection theorem
- Measure
- Semidefinite programming
- The Erdős–Ko–Rado theorem
ASJC Scopus subject areas
- Software
- Mathematics(all)
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Suda, S., Tanaka, H., & Tokushige, N. (2017). A semidefinite programming approach to a cross-intersection problem with measures. Mathematical Programming, 166(1-2), 113-130. https://doi.org/10.1007/s10107-016-1106-3