Avoiding rainbow induced subgraphs in edge-colorings

Forbidding Rainbow-colored Stars

We consider an extremal problem motivated by a paper of Balogh [J. Balogh, A remark on the number of edge colorings of graphs, European Journal of Combinatorics 27, 2006, 565–573], who considered edge-colorings of graphs avoiding fixed subgraphs with a prescribed coloring. More precisely, given r ≥ t ≥ 2, we look for n-vertex graphs that admit the maximum number of r-edge-colorings such that 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. ...

Rainbow spanning subgraphs of edge-colored complete graphs

Consider edge-colorings of the complete graph Kn. Let r(n, t) be the maximum number of colors in such a coloring that does not have t edge-disjoint rainbow spanning trees. Let s(n, t) be the maximum number of colors in such a coloring having no rainbow spanning subgraph with diameter at most t. We prove r(n, t) = (n−2 2 )

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

Properly colored subgraphs and rainbow subgraphs in edge-colorings with local constraints

We consider a canonical Ramsey type problem. An edge-coloring of a graph is called m-good if each color appears at most m times at each vertex. Fixing a graph G and a positive integer m, let f(m,G) denote the smallest n such that every m-good edge-coloring of Kn yields a properly edgecolored copy of G, and let g(m,G) denote the smallest n such that every m-good edge-coloring of Kn yields a rain...