Online Graph Coloring for $k$-Colorable Graphs
Ken-ichi Kawarabayashi, Hirotaka Yoneda, Masataka Yoneda

TL;DR
This paper presents new online algorithms for coloring $k$-colorable graphs, significantly improving previous bounds and closing gaps for deterministic and randomized cases, especially for small $k$.
Contribution
It introduces the first major improvements in nearly three decades for online graph coloring bounds for $k$-colorable graphs, including new algorithms and bounds for various $k$.
Findings
Deterministic algorithms for $k eq 2$ with improved color bounds.
Randomized algorithms for $k=2$ with bounds close to the lower limit.
New competitive ratio for online coloring of graphs with $k eq 2$.
Abstract
We study the problem of online graph coloring for -colorable graphs. The best previously known deterministic algorithm uses colors for general and colors for , both given by Kierstead in 1998. In this paper, we finally break this barrier, achieving the first major improvement in nearly three decades. Our results are summarized as follows: (1) case. We provide a deterministic online algorithm to color -colorable graphs with colors, significantly improving the current upper bound of colors. Our algorithm also matches the best-known bound for ( colors). (2) case. We provide a deterministic online algorithm to color -colorable graphs with colors,…
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