Gyárfás has recently constructed an elegant new example of a triangle-free infinite graph <mml:math alttext="$G$" id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math> with infinite chromatic number. We analyze its structure by studying the properties of a nested family of subgraphs <mml:math alttext="$G_n $" id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>G</mml:mi><mml:mi>n</mml:mi></mml:msub></mml:math> whose union is <mml:math alttext="$G$" id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>G</mml:mi></mml:math>.

International Journal of Mathematics and Mathematical Sciences

On the Structure of a Triangle-Free Infinite-Chromatic Graph of Gyarfas

Abstract

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