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- W2014098222 abstract "The Grundy number of a graph G is the largest number of colors used by any execution of the greedy algorithm to color G. The problem of determining the Grundy number of G is polynomial if G is a P4-free graph and NP-hard if G is a P5-free graph. In this article, we define a new class of graphs, the fat-extended P4-laden graphs, and we show a polynomial time algorithm to determine the Grundy number of any graph in this class. Our class intersects the class of P5-free graphs and strictly contains the class of P4-free graphs. More precisely, our result implies that the Grundy number can be computed in polynomial time for any graph of the following classes: P4-reducible, extended P4-reducible, P4-sparse, extended P4-sparse, P4-extendible, P4-lite, P4-tidy, P4-laden and extended P4-laden, which are all strictly contained in the fat-extended P4-laden class." @default.
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- W2014098222 date "2012-12-01" @default.
- W2014098222 modified "2023-10-18" @default.
- W2014098222 title "On the Grundy number of graphs with few <mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML altimg=si10.gif display=inline overflow=scroll><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:math>’s" @default.
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- W2014098222 doi "https://doi.org/10.1016/j.dam.2011.08.016" @default.
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