Proper Colorings of Plane Quadrangulations Without Rainbow Faces

Colorings Of Plane Graphs With No Rainbow Faces

Vertex colorings without rainbow subgraphs

Given a coloring of the vertices of a graph G, we say a subgraph is rainbow if its vertices receive distinct colors. For graph F , we define the F -upper chromatic number of G as the maximum number of colors that can be used to color the vertices of G such that there is no rainbow copy of F . We present some results on this parameter for certain graph classes. The focus is on the case that F is...

Long rainbow cycles in proper edge-colorings of complete graphs

We show that any properly edge-colored Kn contains a rainbow cycle with at least (4/7− o(1))n edges. This improves the lower bound of n/2− 1 proved in [1]. We consider properly edge-colored complete graphs Kn, where two edges with the same color cannot be incident to each other, so each color class is a matching. An important and well investigated special case of proper edge-colorings is a fact...

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.

Rainbow faces in edge-colored plane graphs

A face of an edge colored plane graph is called rainbow if all its edges receive distinct colors. The maximum number of colors used in an edge coloring of a connected plane graph G with no rainbow face is called the edge-rainbowness of G. In this paper we prove that the edge-rainbowness of G equals to the maximum number of edges of a connected bridge face factor H of G, where a bridge face fact...