Abstract
Given a graph G , its edges are said to be exactly x -coloured if we have a surjective map from the edges to some set of colours of size x . Erickson considered the following statement which he denoted P ( c , m ): if the edges of K ω —the complete graph on vertex set N —are exactly c -coloured, then there exists an infinite complete subgraph of K ω whose edges are exactly m -coloured. Ramsey's Theorem states that P ( c , m ) is true for m =1 and all c ⩾1, and can easily be used to show that P ( c , m ) holds when m =2 and c ⩾2. Erickson conjectured that P ( c , m ) is false whenever c > m ⩾3. We prove that given m ⩾3 there exists an integer C ( m ) such that P ( c , m ) is false for all c ⩾ C ( m ).
Published Version
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