Edge colorings of graphs avoiding some fixed monochromatic subgraph with linear Turán number

Edge-colorings of graphs avoiding fixed monochromatic subgraphs with linear Turán number

Ramsey-type results for Gallai colorings

A Gallai-coloring (G-coloring) is a generalization of 2-colorings of edges of complete graphs: a G-coloring of a complete graph is an edge coloring such that no triangle is colored with three distinct colors. Here we extend some results known earlier for 2-colorings to G-colorings. We prove that in every G-coloring of Kn there exists each of the following: 1. a monochromatic double star with at...

Edge-colorings avoiding rainbow and monochromatic subgraphs

For two graphs G and H , let the mixed anti-Ramsey numbers, maxR(n; G, H), (minR(n; G, H)) be the maximum (minimum) number of colors used in an edge-coloring of a complete graph with n vertices having no monochromatic subgraph isomorphic to G and no totally multicolored (rainbow) subgraph isomorphic to H . These two numbers generalize the classical anti-Ramsey and Ramsey numbers, respectively. ...

On Colorings Avoiding a Rainbow Cycle and a Fixed Monochromatic Subgraph

Let H and G be two graphs on fixed number of vertices. An edge coloring of a complete graph is called (H,G)-good if there is no monochromatic copy of G and no rainbow (totally multicolored) copy of H in this coloring. As shown by Jamison and West, an (H,G)-good coloring of an arbitrarily large complete graph exists unless either G is a star or H is a forest. The largest number of colors in an (...

On monochromatic subgraphs of edge-colored complete graphs

In a red-blue coloring of a nonempty graph, every edge is colored red or blue. If the resulting edge-colored graph contains a nonempty subgraph G without isolated vertices every edge of which is colored the same, then G is said to be monochromatic. For two nonempty graphs G and H without isolated vertices, the monochromatic Ramsey number mr(G,H) of G and H is the minimum integer n such that eve...