Queen Labelings

Abstract

We introduce and investigate the concept of Queen labeling a digraph and its connection to the well-known n-queens problem. In the general case we obtain an upper bound on the size of a queen graph and show that it is tight. We also examine the existence of possible forbid-den subgraphs for this problem and show that only two such subgraphs exist. Then we focus on specific graph families: First we show that every star is a queen graph by giving an algorithm for which we prove cor-rectness. Then we show that the problem of queen labeling a matching is equivalent to a variation of the n-queens problem, which we call the rooks-and-queens problem and we use that fact to give a short proof that every matching is a queen graph. Finally, for unions of 3-cycles we give a general solution of the problem for graphs of n(n - 1) vertices.