Disjoint Cross Intersecting Families
Nuttanon Songsuwan, Supida Sengsamak, Nutchapol Jeerawattana, Thiradet, Jiarasuksakun, Pawaton Kaemawichanurat

TL;DR
This paper investigates the structure of disjoint cross intersecting families of r-subsets, providing new bounds on their combined size and demonstrating limitations of compression techniques in certain cases.
Contribution
It introduces a novel technique to bound the sum of sizes of disjoint cross intersecting families, overcoming limitations of traditional compression methods.
Findings
Established an upper bound for the sum of sizes of disjoint cross intersecting families.
Provided a counterexample showing compression is not always applicable.
Proved the bound is asymptotically sharp.
Abstract
For positive integers and such that , let be a set of elements and let be the family of all -subsets of . Two sub-families and of are called cross intersecting if for all and . One of main tools in the study of extremal set theory, and cross intersecting families in particular, is compression operation. In this paper, we give an example of cross intersecting families and that the compression operation is not applicable when and are disjoint. We develop new technique to prove that, for disjoint cross intersecting families and of , where and $p =…
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Taxonomy
TopicsLimits and Structures in Graph Theory · Mathematical Approximation and Integration · Italy: Economic History and Contemporary Issues
