Extraction Theorems With Small Extraction Numbers

TL;DR

This paper introduces Extraction Theorems for specific geometric object classes, establishing tight bounds on their extraction numbers and providing examples that demonstrate the bounds' optimality.

Contribution

It presents new Extraction Theorems with small, tight bounds for classes like intervals, segments, rays, and octants, advancing geometric combinatorics.

Findings

Established small bounds on extraction numbers for various geometric classes

Proved the tightness of bounds with matching lower bound examples

Extended the understanding of extraction properties in geometric objects

Abstract

In this work, we develop Extraction Theorems for classes of geometric objects with small extraction numbers. These classes include intervals, axis-parallel segments, axis-parallel rays, and octants. We investigate these classes of objects and prove small bounds on the extraction numbers. The tightness of these bounds is demonstrated by examples with matching lower bounds.