The Ramsey number of an \(n\)-edge graph versus triangle is at most \(2n+1\)
The Ramsey number \(r(H,G)\) is defined as the minimal \(N\) such that for any coloring of the edges of the \(N\)-vertex complete graph \(K_ N\) in red and blue, it must contain either a red \(H\) or a blue \(G\). We prove the conjecture of Harary that for any graph \(G\) with \(n\) edges and without isolated vertices, \(r(K_ 3,G)\leq 2n+1\).
scientific article; zbMATH DE number 572444