Sperner type lemma for quadrangulations

TL;DR

This paper generalizes Sperner's lemma from triangulations to quadrangulations, extending the combinatorial topological results to a broader class of polygonal decompositions.

Contribution

It introduces a Sperner-type lemma applicable to quadrangulations, expanding the scope of combinatorial topology results beyond triangulations.

Findings

Established a Sperner-type lemma for quadrangulations

Proved the existence of fully colored quadrilaterals under Sperner coloring

Extended combinatorial topological methods to new polygonal decompositions

Abstract

Sperner's lemma states that every Sperner coloring of a triangulation of a simplex contains a fully colored simplex. We present a generalization of this lemma, where instead of triangulations are considered quadrangulations.