Publisher DOI: 10.1016/j.procs.2021.11.055
Title: Maximum size of r-cross t-intersecting families
Language: English
Authors: Gupta, Pranshu 
Mogge, Yannick 
Piga, Simón 
Schülke, Bjarne 
Keywords: Erdos-Ko-Rado;Extremal set theory;Hilton-Milner;intersecting families
Issue Date: May-2021
Source: 11th Latin and American Algorithms, Graphs and Optimization Symposium (LAGOS 2021)
Abstract (english): 
Given r families of subsets of a fixed n-set, we say that they are r-cross t-intersecting if for every choice of representatives, exactly one from each family, the common intersection of these representatives is of size at least t. We obtain a generalisation of a result by Hilton and Milner on cross intersecting families. In particular, we determine the maximum possible sum of the sizes of non-empty r-cross t-intersecting families in the case when all families are k-uniform and in the case when they are arbitrary subfamilies of the power set. Only some special cases of these results had been proved before. The method we use also yields more general results concerning measures of families instead of their sizes.
Conference: 11th Latin and American Algorithms, Graphs and Optimization Symposium, LAGOS 2021 
ISSN: 1877-0509
Institute: Mathematik E-10 
Document Type: Chapter/Article (Proceedings)
Journal: Procedia computer science 
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