Researches on polychromatic coloring of graphs on surfaces by local transformations

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540117
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: General mathematics (including Probability theory/Statistical mathematics)
• Research Institution: Yokohama National University
• Principal Investigator: NAKAMOTO Atsuhiro 横浜国立大学, 環境情報研究科(研究院), 准教授 (20314445)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 局所変形 / 曲面 / グラフ彩色 / 三角形分割 / 四角形分割 / 偶三角形分割

Outline of Final Research Achievements

In this research, we dealt with polychromatic coloring of graphs on surfaces. This notion was defined in relation with the so called ``Art gallery problem", and my research purpose is to firstly solve the polychromatic 4-chromaticity of cubic bipartite plane graphs by using local transformations, and secondly to solve the similar problems for even-sided maps on other surfaces as its analogy. As a result, we could solve all problems given in the application as we expected. On the other hand, we found a relation of our result to the extension problem of graphs, and got a new direction for the research to use an algebraic method such as a Z2-homology of a surface and the cycle space of graphs. We have been able to obtain much more than we expected before.

Free Research Field

グラフ理論