English

Fully Dynamic $(\Delta+1)$-Coloring in Constant Update Time

Data Structures and Algorithms 2019-10-07 v1

Abstract

The problem of (vertex) (Δ+1)(\Delta+1)-coloring a graph of maximum degree Δ\Delta has been extremely well-studied over the years in various settings and models. Surprisingly, for the dynamic setting, almost nothing was known until recently. In SODA'18, Bhattacharya, Chakrabarty, Henzinger and Nanongkai devised a randomized data structure for maintaining a (Δ+1)(\Delta+1)-coloring with O(logΔ)O(\log \Delta) expected amortized update time. In this paper, we present a (Δ+1)(\Delta+1)-coloring data structure that achieves a constant amortized update time and show that this time bound holds not only in expectation but also with high probability.

Keywords

Cite

@article{arxiv.1910.02063,
  title  = {Fully Dynamic $(\Delta+1)$-Coloring in Constant Update Time},
  author = {Sayan Bhattacharya and Fabrizio Grandoni and Janardhan Kulkarni and Quanquan C. Liu and Shay Solomon},
  journal= {arXiv preprint arXiv:1910.02063},
  year   = {2019}
}
R2 v1 2026-06-23T11:34:52.455Z