A general (rectangular) partition is a partition of a rectangle into an arbitrary number of non-overlapping subrectangles. This paper examines vertex colorings using four colors o...
Fix positive integers k , d , k, d such that k /d > k/d 2. If P is a set of vertices in a (k, d)-colorable graph G, and any two vertices of P are separated by distance at leas...
Consider the following communication problem, that leads to a new notion of edge coloring. The communication network is represented by a bipartite multigraph, where the nodes on o...
For a given positive integer k, sr(m, k) denotes the minimal positive integer such that every coloring of [n], n ≥ sr(m, k), that uses each color at most k times, yields a rainb...
A set of pairwise edge-disjoint triangles of an edge-colored Kn is r-color avoiding if it does not contain r monochromatic triangles, each having a different color. Let fr(n) be th...