In this paper we study the number of vertex recolorings that an algorithm needs to perform in order to maintain a proper coloring of a graph under insertion and deletion of vertices and edges. We present two algorithms that achieve different trade-offs between the number of recolorings and the number of colors used. For any d > 0, the first algorithm maintains a proper O(CdN1/d)-coloring while recoloring at most O(d) vertices per update, where C and N are the maximum chromatic number and maximum number of vertices, respectively. The second algorithm reverses the trade-off, maintaining an O(Cd)-coloring with O(dN1/d) recolorings per update. We also present a lower bound, showing that any algorithm that maintains a c-coloring of a 2-colorable graph on N vertices must recolor at least Ω(N 2/ c(c−1)) vertices per update, for any constant c ≥ 2.
CITATION STYLE
Barba, L., Cardinal, J., Korman, M., Langerman, S., Van Renssen, A., Roeloffzen, M., & Verdonschot, S. (2017). Dynamic graph coloring. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10389 LNCS, pp. 97–108). Springer Verlag. https://doi.org/10.1007/978-3-319-62127-2_9
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