Study on Algorithmic Graph Theory and Mathematical Optimization

2014 Fiscal Year Final Research Report

• Project/Area Number: 25887007
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: University of Tsukuba
• Principal Investigator: SANO Yoshio 筑波大学, システム情報系, 助教 (20650261)
• Project Period (FY): 2013-08-30 – 2015-03-31
• Keywords: グラフ理論 / 競争グラフ / グラフの競争数 / 交叉グラフ / グラフ固有値 / ホフマン・グラフ / トラベル・グルーポイド

Outline of Final Research Achievements

In this research, I studied graphs that are represented as the intersection graphs of some specified set families by using combinatorial, matrix theoretical, and algebraic methods. More concretely, I studied on (1) competition graphs and related notions, (2) graphs with bounded smallest eigenvalues and Hoffman graphs, and (3) travel groupoids which are algebraic structures defined on graphs, and I obtained several new results for each research field.

Free Research Field

離散数学