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- W2602246102 abstract "A dynamic colouring of a graph is a proper colouring in which no neighbourhood of a non-leaf vertex is monochromatic. The dynamic colouring number χ2(G) of a graph G is the least number of colours needed for a dynamic colouring of G. Montgomery conjectured that χ2(G)≤χ(G)+2 for all regular graphs G, which would significantly improve the best current upper bound χ2(G)≤2χ(G). In this note, however, we show that this last upper bound is sharp by constructing, for every integer n≥2, a regular graph G with χ(G)=n but χ2(G)=2n. In particular, this disproves Montgomery’s conjecture." @default.
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- W2602246102 date "2017-10-01" @default.
- W2602246102 modified "2023-09-24" @default.
- W2602246102 title "A counterexample to Montgomery’s conjecture on dynamic colourings of regular graphs" @default.
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- W2602246102 doi "https://doi.org/10.1016/j.dam.2017.05.004" @default.
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