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A study on local deformations for graphs on surfaces focusing on algebraic invariants

Research Project

Project/Area Number 21740088
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeSingle-year Grants
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionNiigata University (2011)
Tsuruoka National College of Technology (2009-2010)

Principal Investigator

SUZUKI Yusuke  新潟大学, 自然科学系, 准教授 (10390402)

Project Period (FY) 2009 – 2011
Project Status Completed (Fiscal Year 2011)
Budget Amount *help
¥2,860,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥660,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywords偶三角形分割 / 閉曲面 / 三角形分割 / 四角形分割 / モノドロミー / 局所変形 / グラフ / Y-rotation / 射影平面
Research Abstract

Although there are many results on diagonal flips for triangulations on surfaces, it becomes difficult if we consider a local deformation for even triangulations or quadrangulations which preserves the regularity of those graphs(algebraic invariants for graphs on surfaces should be focused in this case). We considered problems around here and could obtain some results on them. Especially, we proved that any two k-minimal quadrangulations on the projective plane can be transformed into each other by a sequence of Y-rotations.

Report

(4 results)
  • 2011 Annual Research Report   Final Research Report ( PDF )
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (40 results)

All 2012 2011 2010 2009

All Journal Article (22 results) (of which Peer Reviewed: 22 results) Presentation (18 results)

  • [Journal Article] Y-rotation in k-minimal quadrangulations on the projective plane2012

    • Author(s)
      A. Nakamoto and Y. Suzuki
    • Journal Title

      J. Graph Theory

      Volume: 69 Pages: 301-313

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Y-rotation in k-minimal quadrangulations on the projective plane2012

    • Author(s)
      鈴木有祐, 中本敦浩
    • Journal Title

      Journal of Graph Theory

      Volume: 69 Issue: 3 Pages: 301-313

    • DOI

      10.1002/jgt.20583

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Re-embedding structures of 4-connected projective planar graphs2011

    • Author(s)
      Y. Suzuki
    • Journal Title

      J. Graph Theory

      Volume: 68 Pages: 213-228

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The 2-extendability of 5-connected graphs on surfaces with large representativity2011

    • Author(s)
      K. Kawarabayashi, S. Negami, M. Plummer, and Y. Suzuki
    • Journal Title

      J. Combin. Theory

      Volume: 101 Pages: 206-213

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The 2-extendability of 5-connected graphs on surfaces with large representativity2011

    • Author(s)
      鈴木有祐, 他3名
    • Journal Title

      Journal of Combinatorial Theory, Series B

      Volume: 101 Issue: 4 Pages: 206-213

    • DOI

      10.1016/j.jctb.2011.02.001

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Re-embedding structures of 4-connected projective planar graphs2011

    • Author(s)
      鈴木有祐
    • Journal Title

      Journal of Graph Theory

      Volume: 68 Issue: 3 Pages: 213-228

    • DOI

      10.1002/jgt.20553

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] No optimal 1-planar graph triangulates the non-orientable closed surface of genus 42010

    • Author(s)
      K. Ishiguro, S. Negami, Y. Suzuki and K. Yamamoto
    • Journal Title

      Congressus Numernatium

      Volume: 202 Pages: 25-31

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Re-embeddings of maximum 1-planar graphs2010

    • Author(s)
      Y. Suzuki
    • Journal Title

      SIAM J. Discrete Math.

      Volume: 24 Pages: 1527-1540

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The2-extendability of 5-connected graphson the Klein bottle2010

    • Author(s)
      S. Negami and Y. Suzuki
    • Journal Title

      Discrete Math.

      Volume: 310 Pages: 2510-2518

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] K6-Minors in triangulations on the nonorientable surface of genus 32010

    • Author(s)
      R. Mukae, A. Nakamoto, Y. Oda and Y. Suzuki
    • Journal Title

      Graphs Combin.

      Volume: 26 Pages: 559-570

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] The 2-extendability of graphs on the projective plane, the torus and the Klein bottle2010

    • Author(s)
      I. Mizukai, S. Negami and Y. Suzuki
    • Journal Title

      Graphs Combin.

      Volume: 26 Pages: 549-557

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Diagonal slides and diagonal rotations in quadrangulations on the sphere2010

    • Author(s)
      A. Nakamoto and Y. Suzuki
    • Journal Title

      Yokohama Math. J.

      Volume: 55 Pages: 105-112

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Optimal 1-planar graphs which triangulate other surfaces2010

    • Author(s)
      Y. Suzuki
    • Journal Title

      Discrete Math.

      Volume: 310 Pages: 6-11

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] Optimal 1-planar graphs which triangulate other surfaces2010

    • Author(s)
      鈴木有祐
    • Journal Title

      Discrete Mathematics

      Volume: 310 Pages: 6-11

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Diagonal slides and diagonal rotations in quadrangulations on the sphere2010

    • Author(s)
      鈴木有祐, 中本敦浩
    • Journal Title

      Yokohama Mathematical Journal

      Volume: 55 Pages: 105-112

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The 2-extendability of graphs on the projective plane, the torus and the Klein bottle2010

    • Author(s)
      鈴木有祐, 他2名
    • Journal Title

      Graphs and Combinatorics

      Volume: 26 Pages: 549-557

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] K6-Minors in triangulations on the nonorientable surface of genus 32010

    • Author(s)
      鈴木有祐, 他3名
    • Journal Title

      Graphs and Combinatorics

      Volume: 26 Pages: 559-570

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The 2-extendability of 5-connected graphs on the Klein bottle2010

    • Author(s)
      鈴木有祐, 根上生也
    • Journal Title

      Discrete Mathematics

      Volume: 310 Pages: 2510-2518

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Re-embeddings of maximum 1-planar graphs2010

    • Author(s)
      鈴木有祐
    • Journal Title

      SIAM Journal on Discrete Mathematics

      Volume: 24 Pages: 1527-1540

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] No optimal 1-planar graph triangulates the non-orientable surface of genus 42010

    • Author(s)
      鈴木有祐, 他3名
    • Journal Title

      Congressus Numerantium

      Volume: 202 Pages: 25-31

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] N-Flips in even triangulations on surfaces2009

    • Author(s)
      K. Kawarabayashi, A. Nakamoto and Y. Suzuki
    • Journal Title

      J. Combin. Theory, Ser. B.

      Volume: 99 Pages: 229-246

    • Related Report
      2011 Final Research Report
    • Peer Reviewed
  • [Journal Article] N-Flips in even triangulations on surfaces2009

    • Author(s)
      鈴木有祐, 他2名
    • Journal Title

      Journal of Combinatorial Theory, Series B 99

      Pages: 229-246

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Presentation] The number of edges of maximal 1-planar, graphs and embeddings2012

    • Author(s)
      鈴木有祐
    • Organizer
      渡辺守先生ご退職記念関西グラフ理論研究集会
    • Place of Presentation
      加計国際学術交流センター
    • Year and Date
      2012-03-08
    • Related Report
      2011 Final Research Report
  • [Presentation] The number of edges of maximal 1-planar graphs and embeddings2012

    • Author(s)
      鈴木有祐
    • Organizer
      渡辺守先生ご退職記念関西グラフ理論研究集会
    • Place of Presentation
      加計国際学術交流センター
    • Year and Date
      2012-03-08
    • Related Report
      2011 Annual Research Report
  • [Presentation] Re-embeddings of optimal 1-embeddings of the projective plane2011

    • Author(s)
      鈴木有祐
    • Organizer
      応用数学合同研究
    • Place of Presentation
      龍谷大学
    • Year and Date
      2011-12-17
    • Related Report
      2011 Final Research Report
  • [Presentation] Re-embeddings of optimal 1-embeddings of projective plane2011

    • Author(s)
      鈴木有祐
    • Organizer
      応用数学合同研究集会
    • Place of Presentation
      龍谷大学
    • Year and Date
      2011-12-17
    • Related Report
      2011 Annual Research Report
  • [Presentation] 射影平面上のoptimal 1-embeddingの再埋蔵について2011

    • Author(s)
      鈴木有祐
    • Organizer
      離散数学とその応用研究集会2011
    • Place of Presentation
      奈良県文化会館
    • Year and Date
      2011-08-02
    • Related Report
      2011 Annual Research Report 2011 Final Research Report
  • [Presentation] Optimal 1-embeddingの再埋蔵列挙プログラムについて2010

    • Author(s)
      鈴木有祐
    • Organizer
      第回位相幾何学的グラフ理論研究集会
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2010-11-13
    • Related Report
      2011 Final Research Report
  • [Presentation] Optimal 1-embeddingの再埋蔵列挙プログラムについて2010

    • Author(s)
      鈴木有祐
    • Organizer
      第22回位相幾何学的グラフ理論研究集会
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2010-11-13
    • Related Report
      2010 Annual Research Report
  • [Presentation] On properties of maximal 1-planar graphs2010

    • Author(s)
      鈴木有祐
    • Organizer
      日本数学会・秋季総合分科会
    • Place of Presentation
      名古屋大学
    • Year and Date
      2010-09-22
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] Generating polyhedral quadrangulations of the projective plane2010

    • Author(s)
      鈴木有祐
    • Organizer
      Sixth Cracow Conference on Graph theory "ZGORZELISKO' 10"
    • Place of Presentation
      Hotel Tatry, Poland
    • Year and Date
      2010-09-16
    • Related Report
      2011 Final Research Report
  • [Presentation] Generating polyhedral quadrangulations of the projective plane2010

    • Author(s)
      鈴木有祐
    • Organizer
      Sixth Cracow Conference on Graph theory "ZGOR ZELISKO 10"
    • Place of Presentation
      Hotel Tatry, Poland
    • Year and Date
      2010-09-16
    • Related Report
      2010 Annual Research Report
  • [Presentation] Generating polyhedral quadrangulations of the projective plane2010

    • Author(s)
      鈴木有祐
    • Organizer
      離散数学とその応用研究集会2010
    • Place of Presentation
      高知大学朝倉キャンパス
    • Year and Date
      2010-07-31
    • Related Report
      2011 Final Research Report 2010 Annual Research Report
  • [Presentation] On properties of maximal 1-planar graphs2010

    • Author(s)
      鈴木有祐
    • Organizer
      岡村治子先生退職記念研究集会
    • Place of Presentation
      甲南大学
    • Year and Date
      2010-03-06
    • Related Report
      2011 Final Research Report 2009 Annual Research Report
  • [Presentation] Re-embeddings of maximum 1-planar graphs2009

    • Author(s)
      鈴木有祐
    • Organizer
      33rd Australasian Conference on Combinatorial Mathematics and Combinatorial Computing
    • Place of Presentation
      The University of Newcastle
    • Year and Date
      2009-12-10
    • Related Report
      2011 Final Research Report 2009 Annual Research Report
  • [Presentation] Maximum 1-planar graphの再埋蔵について2009

    • Author(s)
      鈴木有祐
    • Organizer
      第21回位相幾何学的グラフ理論研究集会
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2009-11-26
    • Related Report
      2011 Final Research Report
  • [Presentation] Maximum 1-planar graph の再埋蔵について2009

    • Author(s)
      鈴木有祐
    • Organizer
      第21回位相幾何学的グラフ理論研究集会
    • Place of Presentation
      横浜国立大学
    • Year and Date
      2009-11-26
    • Related Report
      2009 Annual Research Report
  • [Presentation] Generation of quadrangulations with some conditions on surfaces2009

    • Author(s)
      鈴木有祐
    • Organizer
      離散幾何とその応用研究集会2009
    • Place of Presentation
      茨城大学工学部日立キャンパス
    • Year and Date
      2009-08-07
    • Related Report
      2011 Final Research Report
  • [Presentation] Generation of quadrangulations with some conditions on surfaces2009

    • Author(s)
      鈴木有祐
    • Organizer
      離散幾何とその応用研究集会2009
    • Place of Presentation
      茨城大学工学部
    • Year and Date
      2009-08-07
    • Related Report
      2009 Annual Research Report
  • [Presentation] Generation of quadrangulations on surfaces2009

    • Author(s)
      鈴木有祐
    • Organizer
      離散幾何とグラフ理論1日研究集会
    • Place of Presentation
      東海大学教育開発研究所
    • Year and Date
      2009-05-23
    • Related Report
      2011 Final Research Report 2009 Annual Research Report

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Published: 2009-04-01   Modified: 2016-04-21  

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