The Ramsey size number of dipaths
Let \(H\) be a finite graph. The Ramsey size number of \(H\), \(\widehat r(H,H)\), is the minimum number of edges required to construct a graph such that when its edges are 2-colored it contains a monochromatic subgraph isomorphic to \(H\). The main result of this paper is Theorem 1: \({(n-5/2)^2\over 2}\leq\widehat r(\vec P_n,\vec P_n)\), where \(\vec P_n\) denotes the directed path with \(n\) edges.
scientific article; zbMATH DE number 1838984