Ramseyan Properties of Graphs

Ermelinda DeLaVina, Siemion Fajtlowicz

Abstract


Every graph of chromatic number $k$ with more than $k(r-1)(b-1)$ vertices has a $b$-element independent set of vertices such that if any two of them are joined by an edge then the chromatic number stays the same or a $r$-element independent set of vertices such that joining any two of them by an edge increases the chromatic number.


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