K. Kawarabayashi

activity

20242026

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3 papers · 1 filter

cs.DS2025

Online Graph Coloring for $k$ -Colorable Graphs

Ken-ichi Kawarabayashi, Hirotaka Yoneda, Masataka Yoneda

We study the problem of online graph coloring for $k$ -colorable graphs. The best previously known deterministic algorithm uses $O (n^{1 - \frac{1}{k !}})$ colors for genera…

math.CO2025

5-Coloring Planar Graphs with a Color Class of Order at Most $∣ V ∣/6$

Yuta Inoue, Ken-ichi Kawarabayashi, Atsuyuki Miyashita

We show that any planar graph $G = (V, E)$ has a 5-coloring such that one color class contains at most $∣ V ∣/6$ vertices. In other words, there exists a partition of $V$ into five inde…

math.CO2025

Three-edge-coloring (Tait coloring) cubic graphs on the torus: A proof of Grünbaum's conjecture

Yuta Inoue, Ken-ichi Kawarabayashi, Atsuyuki Miyashita +2

We prove that every cyclically 4-edge-connected cubic graph that can be embedded in the torus, with the exceptional graph class called "Petersen-like", is 3-edge-colorable. This me…

Online Graph Coloring for k-Colorable Graphs

5-Coloring Planar Graphs with a Color Class of Order at Most ∣V∣/6

Three-edge-coloring (Tait coloring) cubic graphs on the torus: A proof of Grünbaum's conjecture

Online Graph Coloring for $k$ -Colorable Graphs

5-Coloring Planar Graphs with a Color Class of Order at Most $∣ V ∣/6$