Ramsey numbers for unions of some cycles
Let G and H be two graphs and let r(G,H) denote the Ramsey number defined as follows: r(G,H) is the smallest positive integer p so that, if the edges of the complete graph on p vertices are colored with two colors then either there is a subgraph isomorphic to G with all of its edges colored with the first color or a subgraph isomorphic to H with all of its edges colored with the second color. In this paper, the authors compute the exact values for \(r(C_ 4\cup C_ m\), \(C_ 4\cup C_ n)\), \(r(mC_ n\), \(mC_ 4)\), \(r(m(C_ 3\cup C_ 4)\), \(n(C_ 3\cup C_ 4))\) for most values of m and n.
scientific article; zbMATH DE number 4035875