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Abstract <p>The paper describes a new method for constructing triangle-free graphs with an arbitrarily large chromatic number. The method is substantiated using properties of various types of ultrafilter extensions of functions and predicates.</p>

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On a Combinatorial Application of Ultrafilter Theory: A New Construction of Triangle-Free Graphs with Arbitrarily Large Chromatic Number

  • 期刊论文

  • 发表日期：

    2025年4月1日

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  • N. L. Polyakov

摘要

Abstract

The paper describes a new method for constructing triangle-free graphs with an arbitrarily large chromatic number. The method is substantiated using properties of various types of ultrafilter extensions of functions and predicates.