Improved Bound on Sets Including No Sunflower with Three Petals
Junichiro Fukuyama

TL;DR
This paper presents a new combinatorial approach to bound the size of set families avoiding 3-sunflowers, improving understanding of sunflower conjectures and providing an alternative proof for existing bounds.
Contribution
It introduces a novel combinatorial method to establish bounds on set families avoiding 3-sunflowers, offering an alternative proof to previous results.
Findings
Proves that set families satisfying a specific combinatorial condition contain three disjoint sets.
Provides an alternative proof for the 3-sunflower bound using a different combinatorial approach.
Improves the theoretical understanding of sunflower conjectures and related combinatorial bounds.
Abstract
A sunflower with petals, or -sunflower, is a family of sets every two of which have a common intersection. Known since 1960, the sunflower conjecture states that a family of sets each of cardinality includes a -sunflower if for some depending only on . The case of the conjecture was especially emphasized by Erd\"os, for which Kostochka's bound on without a 3-sunflower had been the best-known since 1997 until the recent development to update it to . This paper proves with an entirely different combinatorial approach that includes three mutually disjoint sets if it satisfies the -condition for any given . Here is a…
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Taxonomy
TopicsLimits and Structures in Graph Theory · Advanced Graph Theory Research · graph theory and CDMA systems
