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- W4286890962 abstract "The Grundy number of a graph is the maximum number of colours used by the ``First-Fit'' greedy colouring algorithm over all vertex orderings. Given a vertex ordering $sigma= v_1,dots,v_n$, the ``First-Fit'' greedy colouring algorithm colours the vertices in the order of $sigma$ by assigning to each vertex the smallest colour unused in its neighbourhood. By restricting this procedure to vertex orderings that are connected, we obtain {em connected greedy colourings}. For some graphs, all connected greedy colourings use exactly $chi(G)$ colours; they are called {em good graphs}. On the opposite, some graphs do not admit any connected greedy colouring using only $chi(G)$ colours; they are called {em ugly graphs}. We show that no perfect graph is ugly. We also give simple proofs of this fact for subclasses of perfect graphs (block graphs, comparability graphs), and show that no $K_4$-minor free graph is ugly." @default.
- W4286890962 created "2022-07-25" @default.
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- W4286890962 date "2021-10-26" @default.
- W4286890962 modified "2023-09-23" @default.
- W4286890962 title "Connected greedy colourings of perfect graphs and other classes: the good, the bad and the ugly" @default.
- W4286890962 doi "https://doi.org/10.48550/arxiv.2110.14003" @default.
- W4286890962 hasPublicationYear "2021" @default.
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