TY - JOUR
T1 - A semidefinite programming approach to a cross-intersection problem with measures
AU - Suda, Sho
AU - Tanaka, Hajime
AU - Tokushige, Norihide
N1 - Funding Information:
Acknowledgements The authors thank Peter Frankl for telling them the reference [5]. They also thank the anonymous referees for comments and suggestions. Hajime Tanaka was supported by JSPS KAKENHI Grant No. 25400034. Norihide Tokushige was supported by JSPS KAKENHI Grant No. 25287031.
PY - 2017/11/1
Y1 - 2017/11/1
N2 - 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.
AB - 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.
KW - Cross-intersecting families
KW - Intersection theorem
KW - Measure
KW - Semidefinite programming
KW - The Erdős–Ko–Rado theorem
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U2 - 10.1007/s10107-016-1106-3
DO - 10.1007/s10107-016-1106-3
M3 - Article
AN - SCOPUS:85007572082
VL - 166
SP - 113
EP - 130
JO - Mathematical Programming
JF - Mathematical Programming
SN - 0025-5610
IS - 1-2
ER -