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Autotopism stabilized colouring games on rook's graphs

 

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Opened Access Autotopism stabilized colouring games on rook's graphs
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Author: Andres, Stephan Dominique
Falcón Ganfornina, Raúl Manuel
Department: Universidad de Sevilla. Departamento de Matemática Aplicada I (ETSII)
Date: 2017-06-29
Published in: The Second Malta Conference in Graph Theory and Combinatorics (2017),
Document type: Presentation
Abstract: Based on the fact that every partial colouring of the rook’s graph Kr✷Ks is uniquely related to an r × s partial Latin rectangle, this work deals with the Θ-stabilized colouring game on the graph Kr✷Ks. This is a variant of the classical colouring game on finite graphs [1,2,6,7] so that each move must respect a given autotopism Θ of the resulting partial Latin rectangle. The complexity of this variant is examined by means of its Θ-stabilized game chromatic number, which depends in turn on the cycle structure of the autotopism under consideration. Based on the known classification of such cycle structures [3,4,5,8], we determine in a constructive way the game chromatic number associated to those rook’s graphs Kr✷Ks, for which r ≤ s ≤ 8.
Cite: Andres, S.D. y Falcón Ganfornina, R.M. (2017). Autotopism stabilized colouring games on rook's graphs. En The Second Malta Conference in Graph Theory and Combinatorics, Qawra, Malta.
Size: 7.663Mb
Format: PDF

URI: https://hdl.handle.net/11441/69147

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