Toward a Graph Version of Rado's Theorem

[摘要] 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.

[学科分类] 离散数学和组合数学

[关键词] coloring;graph theory;Ramsey theory;Rado's theorem