3 papers
math.CO2026
Three-edge-coloring apex cubic graphs
Yuta Inoue, Ken-ichi Kawarabayashi, Rintaro Matsuo +3
A graph is \emph{apex} if has a vertex such that is planar. We prove that every -connected apex cubic graph is three-edge-colorable. This result gives the fina…
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…
math.CO2024
Three-edge-coloring projective planar cubic graphs: A generalization of the Four Color Theorem
Yuta Inoue, Ken-ichi Kawarabayashi, Atsuyuki Miyashita +2
We prove that every cyclically 4-edge-connected cubic graph that can be embedded in the projective plane, with the single exception of the Petersen graph, is 3-edge-colorable. In o…