Helly-type theorems for separated d-intervals

2025/01/06 by Rao, Wei · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2501.03207

Abstract

A separated d-interval is defined as a disjoint union of d convex sets from the real line \mathbb R. In this paper, we establish a series of Helly-type theorems for convexity spaces derived from separated d-intervals. Our results encompass the Radon number, Helly number, colorful Helly number, fractional Helly number, colorful fractional Helly theorem, (p,q) theorem, and two kinds of colorful (p,q) theorems for these convexity spaces. The primary tools employed in our proofs involve simplicial complexes and collapsibility.

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• Strong invariants and Tverberg numbers in convexity spaces

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