Coloring of graphs on surfaces using Hamiltonian cycles with Topological property

2022 Fiscal Year Final Research Report

• Project/Area Number: 18K03391
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12030:Basic mathematics-related
• Research Institution: Yokohama National University
• Principal Investigator: Ozeki Kenta 横浜国立大学, 大学院環境情報研究院, 准教授 (10649122)
• Project Period (FY): 2018-04-01 – 2023-03-31
• Keywords: Hamiltonian cycle / Coloring

Outline of Final Research Achievements

The purpose of this study is to propose a new method of coloring graphs on surfaces using Hamiltonian cycles. To achieve this goal, we investigated Hamiltonian cycles and related structures, and discussed various coloring schemes based on them.
For example, the Kempe change is an important research subject because it is used in the proof of the Four-Color Theorem. We will publish new results about that in 2022. Like this, we have conducted research on cycles and coloring, and have achieved the publication of more than 20 papers during the research period.

Free Research Field

グラフ理論

Academic Significance and Societal Importance of the Research Achievements

グラフの彩色は，スケジューリングや電波の周波数割り当て問題も利用される重要な研究対象である．また，有名な四色定理から，特に平面や閉曲面上のグラフの彩色問題が，グラフ理論において長らく研究されてきたが，研究が進んでいない分野も存在している．本研究では，ハミルトン閉路を利用した新しい彩色の手法について考察し，様々な成果を得た．これにより，グラフの閉路と彩色の研究が進展したといえる．