On factor problems in graphs with high regularity

2016 Fiscal Year Final Research Report

• Project/Area Number: 26800085
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Foundations of mathematics/Applied mathematics
• Research Institution: Keio University
• Principal Investigator: FUJISAWA Jun 慶應義塾大学, 商学部(日吉), 准教授 (00516099)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: グラフ / 位相幾何学的グラフ理論 / 因子問題 / マッチング

Outline of Final Research Achievements

The following is the main part of the results obtained in this research. Firstly, as for the problem of determining whether every 5-connected projective planar triangulation is distance d m-extendable or not, we solved the d=4 case. Secondly, in 5-connected planar graphs with at most two non-triangular faces, we obtained the best threshold on distance matching extendability, which was not shown in the former research. Thirdly, it turned out that highly locally-connected star free graphs of even order have the property such that every matching in which the edges lie pairwise distance far apart is extendable.

Free Research Field

数物系科学