| Project/Area Number |
16K05254
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Foundations of mathematics/Applied mathematics
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| Research Institution | Kochi University |
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Principal Investigator |
Suzuki Kazuhiro 高知大学, 教育研究部自然科学系理工学部門, 講師 (50514410)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | グラフ理論 / 辺着色 / 辺彩色 / 単色 / 虹色 / (g,f)-着色 / 全域木 / 完全グラフ / 虹色全域木 / (g,f)-着色全域木 / 異色全域木 / 異色全域林 / (g,f)異色全域木 / (g,f)異色全域林 / 離散数学 / 離散幾何学 |
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| Outline of Final Research Achievements |
Let g and f be mappings from a color set to the set of non-negative integers. A graph with at least g(c) and at most f(c) edges for each color c is said to be (g,f)-chromatic graph. In this study, we showed a sufficient condition for an edge-colored complete graph to have a (g,f)-chromatic spanning forest with exactly m components, and a necessary and sufficient condition for an edge-colored complete graph G to have a spanning tree whose the color distribution ratio is the same as that of G. Moreover, we showed that any edge-colored complete graph G has a spanning tree whose the color distribution ratio is similar to that of G. We conjectured that any edge-colored complete graph G of order 2n can be decomposed into n edge-disjoint spanning trees where each tree has a color distribution ratio similar to that of G, and showed that it is true for a special coloring of G.
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| Academic Significance and Societal Importance of the Research Achievements |
すべての色が異なるグラフを虹色グラフという。言い換えればどの色も高々1本までしか塗られていないグラフである。本研究の貢献の一つは、虹色部分グラフを一般化した(g,f)-部分グラフを定義することで辺着色グラフ研究の研究対象を広げたことである。この定義により、各色ごとに塗られていても良い辺の数をコントロールできるようになり応用範囲が広がることが期待できる。例えば、通信ネットワーク等、複数のタイプのノードやリンクで構成されたヘテロジニアスネットワーク（heterogeneous network）が持つべき部分構造の分析は、タイプを色と見なした(g,f)-着色部分グラフの問題に帰着できるかもしれない。
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