Dynamic graph coloring
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(N2c(c−1)) vertices per update, for any constant c≥2.
|Series||Lecture Notes in Computer Science|
Barba, L. (Luis), Cardinal, J. (Jean), Korman, M. (Matias), Langerman, S. (Stefan), Van Renssen, A. (André), Roeloffzen, M. (Marcel), & Verdonschot, S. (Sander). (2017). Dynamic graph coloring. In Lecture Notes in Computer Science. doi:10.1007/978-3-319-62127-2_9