### 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 |
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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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## Cite this

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