Erdos's Question on the Independence Ratio of Unit-Distance Graphs
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Statement
Erdos asked whether a finite unit-distance graph in the plane can have independence ratio below . One exists, built on the geometric fractional chromatic number framework of Matolcsi, Ruzsa, Varga and Zsamboki plus a carefully chosen two-vertex augmentation.
Context
A question of Erdos in the Hadwiger-Nelson circle, where the independence ratio bound is a standard measure of progress on colouring the plane.
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