1,508 research outputs found
Remarks on the size of critical edge-chromatic graphs
AbstractWe give new lower bounds for the size of Δ-critical edge-chromatic graphs when 6 ⩽ Δ ⩽ 21
Triangle-free intersection graphs of line segments with large chromatic number
In the 1970s, Erdos asked whether the chromatic number of intersection graphs
of line segments in the plane is bounded by a function of their clique number.
We show the answer is no. Specifically, for each positive integer , we
construct a triangle-free family of line segments in the plane with chromatic
number greater than . Our construction disproves a conjecture of Scott that
graphs excluding induced subdivisions of any fixed graph have chromatic number
bounded by a function of their clique number.Comment: Small corrections, bibliography updat
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