Upper bounds for harmonious colorings
Colin McDiarmid, Luo Xinhua · Journal of Graph Theory · 1991
Abstract A harmonious coloring of a simple graph G is a coloring of the vertices such that adjacent vertices receive distinct colors and each pair of colors appears together on at most one edge. The harmonious chromatic number h(G) is the least number of colors in such a coloring. We improve an upper bound on h(G) due to Lee and Mitchem, and give upper bounds for related quantities.