Title:
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Queen Labelings
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Author:
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Bloom, Gary; Lampis, Michael; Muntaner Batle, Francesc Antoni; Rius Font, Miquel
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada IV; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions |
Abstract:
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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. |
Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística -Graph labelings -Labeling -Grafs, Teoria de -Classificació AMS::05 Combinatorics::05C Graph theory |
Rights:
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Document type:
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Article |
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