Toward a Graph Version of Rado's Theorem

Andy Parrish

Abstract


An equation is called graph-regular if it always has monochromatic solutions under edge-colorings of $K_{\mathbb{N}}$. We present two Rado-like conditions which are respectively necessary and sufficient for an equation to be graph-regular.


Keywords


coloring; graph theory; Ramsey theory; Rado's theorem

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