Yuta Inoue

collaborators

5 papers

math.CO2026

Three-edge-coloring apex cubic graphs

Yuta Inoue, Ken-ichi Kawarabayashi, Rintaro Matsuo +3

A graph $G$ is \emph{apex} if $G$ has a vertex $v$ such that $G - v$ is planar. We prove that every $2$ -connected apex cubic graph is three-edge-colorable. This result gives the fina…

math.CO2026

The Four Color Theorem with Linearly Many Reducible Configurations and Near-Linear Time Coloring

Yuta Inoue, Ken-ichi Kawarabayashi, Atsuyuki Miyashita +3

We give a near-linear time 4-coloring algorithm for planar graphs, improving on the previous quadratic time algorithm by Robertson et al. from 1996. Such an algorithm cannot be ach…

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 GrÃ¼nbaum'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…

math.CO2024

Three-edge-coloring projective planar cubic graphs: A generalization of the Four Color Theorem