期刊
GRAPHS AND COMBINATORICS
卷 31, 期 2, 页码 477-495出版社
SPRINGER JAPAN KK
DOI: 10.1007/s00373-015-1551-4
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资金
- OTKA under ERC [10-EuroGIGA-OP-003]
- Swiss National Science Foundation [200020-144531, 200021-137574]
- OTKA [NN-102029]
- Lendulet project of the Hungarian Academy of Sciences
- EPFL
Given a sequence of positive integers , let denote the family of all sequences of positive integers such that for all . Two families of sequences (or vectors), , are said to be -cross-intersecting if no matter how we select and , there are at least distinct indices such that . We determine the maximum value of over all pairs of -cross-intersecting families and characterize the extremal pairs for , provided that . The case is quite different. For this case, we have a conjecture, which we can verify under additional assumptions. Our results generalize and strengthen several previous results by Berge, Borg, Frankl, Furedi, Livingston, Moon, and Tokushige, and answers a question of Zhang.
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