Yuta Inoue

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20242026

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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…

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

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