University of Miyazaki · Graduate School of Education / Faculty of Education · 准教授

Research keywordsgraph theory・grid embeddings・ordered graphs・triangulations・quadrangulations・projective planar graphs

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• A graph G is said to be grid locatable if it admits a representation such that vertices are mapped to grid points and edges to line segments that avoid grid points but the extremes. Additionally G is said to be properly embeddable in the grid if it is grid locatable and the segments representing edges do not cross each other. We study the area needed to obtain those representations for some graph families. © 2012 Springer-Verlag.2012 · 論文
• For a positive integer k >= 4, a graph G is called k-ordered, if for any ordered set of k distinct vertices of G, G has a cycle that contains all the vertices in the designated order. Goddard (2002) [3] showed that every 4-connected triangulation of the plane is 4-ordered. In this paper, we improve this result; every 4-connected triangulation of any surface is 4-ordered. Our proof is much shorter than the proof by Goddard. (C) 2010 Elsevier B.V. All rights reserved.2002 · 論文
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• Discrete Mathematics論文

• 曲面上のグラフのマイナー関係とその構造に関する研究
• グラフの幾何的極大性に関する研究
• 曲面上のグラフにおける辺極大性と埋め込み構造

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