Queen Labelings
نویسندگان
چکیده
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 forbidden 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 correctness. 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.
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