MUKAE Raiji

写真a

Affiliation

Faculty of Education Mathematics education

Title

Associate Professor

External Link

Research Interests 【 display / non-display

  • Discrete Mathematics

  • Topological Graph Theory

  • Graph Theory

Research Areas 【 display / non-display

  • Natural Science / Basic mathematics

  • Natural Science / Applied mathematics and statistics

External Career 【 display / non-display

  • University of Miyazaki   Faculty of Education   Associate Professor

    2023.2

  • Miyakonojo National College of Technology   General Education   Associate Professor

    2018.4 - 2023.2

  • Kisarazu National College of Technology   Associate Professor

    2017.4 - 2018.3

  • Miyakonojo National College of Technology   General Education   Lecturer

    2012.4 - 2017.3

Professional Memberships 【 display / non-display

  • 日本数学会

    2012.4

 

Papers 【 display / non-display

  • Covering projective planar graphs with three forests Reviewed

    Raiji Mukae, Kenta Ozeki, Terukazu Sano, Ryuji Tazume

    Discrete Mathematics   345 ( 4 )   112748 - 112748   2022

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    Language:English   Publishing type:Research paper (scientific journal)  

    DOI: 10.1016/j.disc.2021.112748

  • 3-Polychromatic quadrangulations on surfaces Reviewed

    Raiji Mukae, Astuhiro Nakamoto, Yusuke Suzuki

    Congressus Numerantium   219   43 - 51   2014

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    Language:English   Publishing type:Research paper (scientific journal)  

  • Compact grid representation of graphs Reviewed

    José Cáceres, Carmen Cortés, Clara Isabel Grima, Masahiro Hachimori, Alberto Márquez, Raiji Mukae, Atsuhiro Nakamoto, Seiya Negami, Rafael Robles, Jesús Valenzuela

    Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)   7579   166 - 174   2012

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    Language:English   Publishing type:Research paper (international conference proceedings)   Publisher:Springer  

    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.

    DOI: 10.1007/978-3-642-34191-5_16

    Scopus

  • 4-connected triangulations and 4-orderedness Reviewed

    Raiji Mukae, Kenta Ozeki

    DISCRETE MATHEMATICS   310 ( 17-18 )   2271 - 2272   2010.9

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:ELSEVIER SCIENCE BV  

    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.

    DOI: 10.1016/j.disc.2010.04.026

    Web of Science

  • K6-Minors in Triangulations on the Nonorientable Surface of Genus 3 Reviewed

    Raiji Mukae, Atsuhiro Nakamoto, Yoshiaki Oda, Yusuke Suzuki

    GRAPHS AND COMBINATORICS   26 ( 4 )   559 - 570   2010.7

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    Language:English   Publishing type:Research paper (scientific journal)   Publisher:SPRINGER TOKYO  

    In this paper, we shall give a constructive characterization of triangulations on the nonorientable surface of genus 3 without K (6)-minors. Our characterization implies that every 5-connected triangulation and every 4-representative triangulation on the surface has a K (6)-minor.

    DOI: 10.1007/s00373-010-0931-z

    Web of Science

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Presentations 【 display / non-display

  • Irreducible edge-maximal maps on the projective plane and the torus International conference

    Raiji Mukae

    35th Workshop on Topological Graph Theory  2023.11.10 

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    Event date: 2023.11.7 - 2023.11.10

    Language:English   Presentation type:Oral presentation (general)  

  • 四色定理とその周辺に関する話題

    向江 頼士

    MZセミナー  2023.5.29 

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    Event date: 2023.5.29

    Presentation type:Oral presentation (general)  

  • Edge-maximal projective-planar and toroidal graphs International conference

    Raiji Mukae

    30th Workshop on Topological Graph Theory (TGT30)  2018.10.26 

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    Event date: 2018.10.24 - 2018.10.26

    Language:English   Presentation type:Oral presentation (general)  

  • Purity of projective planar graphs International conference

    Raiji Mukae, Terukazu Sano

    The 5th International Combinatorics Conference  2017.12.8 

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    Event date: 2017.12.4

    Language:English   Presentation type:Oral presentation (general)  

  • 射影平面上の辺極大なグラフと三角形分割

    向江 頼士

    第29回位相幾何学的グラフ理論研究集会  2017.11.17 

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    Event date: 2017.11.17 - 2017.11.18

    Language:Japanese   Presentation type:Oral presentation (general)  

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Grant-in-Aid for Scientific Research 【 display / non-display

  • グラフの幾何的極大性に関する研究

    Grant number:21K03345  2021.04 - 2024.03

    日本学術振興会  科学研究費助成事業  基盤研究(C)

    向江 頼士

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    Authorship:Principal investigator 

  • 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

    Grant number:10J04050  2010 - 2011

    日本学術振興会  科学研究費助成事業  特別研究員奨励費

    向江 頼士

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    Authorship:Principal investigator 

    1937年,K.Wagnerによって5頂点からなる完全グラフK5をマイナーに持つグラフの構造が特徴付けられたが,6頂点以上の完全グラフに関しては何も知られていない状況であった.ところが,2003年にB.Moharたちは,「グラフが閉曲面に埋め込める」という位相幾何学的な条件を付加することにより,「射影平面上の5-連結3-representativeグラフはK6をマイナーに持つ」という定理を証明した.この結果により,K6をマイナーに持つためのある程度意味のあるグラフ構造が記述されたが,まだ十分条件を与えるに留まっていた.そこで本研究では,曲面上のグラフを「三角形分割(各面が三角形であるような曲面上の単純グラフ)」に限定した.B.Moharたちの定理よりも条件は強くなっているが,射影平面,トーラス,ダブルトーラス,クラインの壷,種数3の向き付け不可能な閉曲面上の三角形分割がK6をマイナーに持つための必要十分条件を示している.これらの結果を皮切りに,完全グラフをマイナーに持つ曲面上のグラフ構造とその関連についての研究を行った.今年度の研究結果の一つとして,種数4の向き付け不可能な閉曲面上の三角形分割がK6をマイナーに持つための必要十分条件を示した.この結果から「種数4の向き付け不可能な閉曲面の全ての5-連結三角形分割と全ての4-representative三角形分割はK6をマイナーに持つ」という系を得られた.
    また,その他の閉曲面上のグラフの研究として,四角形分割から偶三角形分割への拡張可能性についていくつかの結果が得られた.