Queen Labelings
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 pro...
| Autores: | , , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2008 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/2784 |
| Acesso em linha: | https://hdl.handle.net/2117/2784 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Graph labelings Labeling Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística |
| Resumo: | 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. |
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