Recoloring Directed Graphs
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[1] Technical University of Berlin
Technical University of Berlin
Berlin, Stadt, Alemania
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[2] Universitat Politècnica de Catalunya
Universitat Politècnica de Catalunya
Barcelona, España
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- Localización: XIII Encuentros de Geometría Computacional: Zaragoza, del 29 de junio al 1 de julio de 2009 / Alfredo García Olaverri (ed. lit.), Javier Tejel Altarriba (ed. lit.), 2009, ISBN 978-84-92774-11-1, págs. 91-97
- Idioma: inglés
- Texto completo no disponible (Saber más ...)
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Resumen
Let G be a directed graph and k a positive integer. We define the k-color graph of G (Dk(G) for short) as the directed graph having all k-colorings of G as node set, and where two k-colorings and ' are joined by a directed edge ! ' if ' is obtained from by choosing a vertex v and recoloring v so that its color is different from the colors of all its out-neighbors. We investigate reachability questions in Dk(G). In particular we want to know whether a fixed legal k′-coloring of G with k′ k is reachable in Dk(G) from every possible initial k-coloring . Interesting instances of this problem arise when G is planar and the orientation is an arbitrary -orientation for fixed . Our main result is that reachability can be guaranteed if the orientation has maximal out-degree k − 1 and an accessible pseudo-sink.
