2018 Fiscal Year Final Research Report
| Project/Area Number |
16K17646
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Senshu University |
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Principal Investigator |
Tsuchiya Shoichi 専修大学, ネットワーク情報学部, 准教授 (10647564)
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| Project Period (FY) |
2016-04-01 – 2019-03-31
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| Keywords | Halin graph / HIST / fullerene graph / plane graph / tree |
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| Outline of Final Research Achievements |
In this research, we aimed to obtain theorems for the existence of a spanning Halin subgraph. For plane triangulations, we proved that there exists an infinite family of 5-connected plane triangulations without a spanning Halin subgraph. On the other hand, we obtained a theorem on forbidden subgraphs which guarantees the existence of a spanning Halin subgraph. This result is the first positive result for the existence of a spanning Halin subgraph in non-trivial graph classes.
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| Free Research Field |
グラフ理論
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| Academic Significance and Societal Importance of the Research Achievements |
グラフ理論では，木や閉路について多くの成果が発表されている．Halin graphの研究は木と閉路によって構成される構造について議論するため，木の研究と閉路の研究を結び付ける新たな研究が創生できる．そのような意味で，本研究は学術的に意義がある．また，辺の数の少ない連結度の高いグラフは，コストを抑えた強度の高い構造と関連があるため，応用面に活用することも可能である．
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