Restricted extension of sparse partial edge colorings of hypercubes

Interval cyclic edge-colorings of graphs

A proper edge-coloring of a graph G with colors 1, , t  is called an interval cyclic t  coloring if all colors are used, and the edges incident to each vertex ( ) v V G  are colored with ( ) G d v consecutive colors by modulo t , where ( ) G d v is the degree of the vertex v in G . In this paper some properties of interval cyclic edge-colorings are investigated. Also, we give some bounds for...

Vertex Distinguishing Edge- and Total-Colorings of Cartesian and other Product Graphs

This paper studies edgeand total-colorings of graphs in which (all or only adjacent) vertices are distinguished by their sets of colors. We provide bounds for the minimum number of colors needed for such colorings for the Cartesian product of graphs along with exact results for generalized hypercubes. We also present general bounds for the direct, strong and lexicographic products.

On balanced colorings of sparse hypergraphs

We investigate 2-balanced colorings of sparse hypergraphs. As applications, we derive several results on balanced edge-colorings of multigraphs.

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.

On the Defining Number of (2n - 2)-Vertex Colorings of Kn x Kn