Edge-colorings avoiding rainbow and monochromatic subgraphs

Vertex Colorings without Rainbow or Monochromatic Subgraphs

This paper investigates vertex colorings of graphs such that some rainbow subgraph R and some monochromatic subgraph M are forbidden. Previous work focussed on the case that R = M . Here we consider the more general case, especially the case that M = K2.

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

Avoiding rainbow induced subgraphs in edge-colorings

Let H be a fixed graph on k vertices. For an edge-coloring c of H , we say that H is rainbow, or totally multicolored if c assigns distinct colors to all edges of H . We show, that it is easy to avoid rainbow induced graphs H . Specifically, we prove that for any graph H (with some notable exceptions), and for any graphs G, G 6= H , there is an edge-coloring of G with k colors which contains no...

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...

Rainbow copies of C4 in edge-colored hypercubes

For positive integers k and d such that 4 ≤ k < d and k 6= 5, we determine the maximum number of rainbow colored copies of C4 in a k-edge-coloring of the d-dimensional hypercube Qd. Interestingly, the k-edge-colorings of Qd yielding the maximum number of rainbow copies of C4 also have the property that every copy of C4 which is not rainbow is monochromatic.