Existence of 5-chromatic locally planar triangulations on closed surfaces and the weak Grunbaum's conjecture

2021 Fiscal Year Final Research Report

• Project/Area Number: 17K14239
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Tokyo University of Science (2018-2021); Tokyo Denki University (2017)
• Principal Investigator: Noguchi Kenta 東京理科大学, 理工学部情報科学科, 講師 (50748613)
• Project Period (FY): 2017-04-01 – 2022-03-31
• Keywords: グラフ理論 / 閉曲面 / グラフ彩色

Outline of Final Research Achievements

In this research, we investigated graphs embedded on surfaces. Especially, for triangulations and quadrangulations, we did the following:
(1) describing the relationship between them in terms of the chromatic number, (2) showing that every even triangulation of a surface with non-negative Euler characteristic has a Grunbaum coloring, and (3) analysing re-embedding structure of 1-embedded graphs.

Free Research Field

グラフ理論

Academic Significance and Societal Importance of the Research Achievements

数学におけるグラフ理論分野の理論研究を発展させた。