2017 Fiscal Year Final Research Report
Contraction-criticality for the domination number of graphs and application for Vizing's conjecture
| Project/Area Number |
26800086
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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 | Kitasato University (2016-2017)
Tokyo University of Science (2014-2015) |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | グラフ理論 / 支配数 / Vizing予想 / 臨界的グラフ / 多彩支配数 / 直径 / 最大次数 |
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| Outline of Final Research Achievements |
In this research, we focused on the graphs having the domination-criticality for the contraction or addition of edges, or the deletion of vertices, and gave some generalizations for such concepts. By using such new concept, we generalized some theorems concerning upper bounds on the diameter of vertex-deletion critical graphs. Furthermore, we also gave a sufficient condition forcing the rainbow domination of graphs to be trivial value via maximum degree. So we can see when the rainbow domination number is appropriate to be used for a generalization of the domination number.
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| Free Research Field |
グラフ理論
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