Equitable Coloring of Corona Products of Graphs

In many applications in sequencing and scheduling it is desirable to have an underlaying graph as equitably colored as possible. In this paper, we consider an equitable coloring of some corona products H G of two graphs G and H. In particular, we show that deciding the colorability of H G is NP-complete even if G is 4-regular and H is . 2 K Next, we prove exact values or upper bounds on the equitable chromatic number ( ) , H G = χ where G is an equitably 3or 4colorable graph and H is an r-partite graph, a path, a cycle or a complete graph. Our proofs are constructive in that they lead to polynomial algorithms for equitable coloring of such graph products provided that an equitable coloring of G is given. As a by-product we obtain a new class of graphs that confirm Equitable Coloring Conjecture.