A Lov\'asz-Kneser theorem for triangulations

TL;DR

This paper proves that the Kneser graph formed from triangulations of a convex polygon has a chromatic number equal to the polygon's number of vertices minus two, revealing a new combinatorial property.

Contribution

It establishes a Lovász-Kneser type theorem specifically for the graph of triangulations of convex polygons, a novel result in combinatorics.

Findings

Kneser graph of triangulations has chromatic number n-2

Provides a new combinatorial characterization of triangulations

Extends Lovász's theorem to a geometric setting

Abstract

We show that the Kneser graph of triangulations of a convex $n$-gon has chromatic number $n-2$.