We study vertex-colorings of plane graphs that do not contain a rainbow face, i.e., a face with vertices of mutually distinct colors. If G is a 3-connected plane graph with n vert...
Given a simple graph G, a harmonious coloring of G is a proper vertex coloring such that each pair of colors appears together on at most one edge. The harmonious chromatic number i...
A radio coloring of a graph G is an assignment of nonnegative integers to its nodes so that each pair of adjacent nodes have color numbers that differ by at least two, and any pai...
In the minimum path coloring problem, we are given a graph and a set of pairs of vertices of the graph and we are asked to connect the pairs by colored paths in such a way that pa...