Fujisawa, Jun

写真a

Affiliation

Faculty of Business and Commerce (Hiyoshi)

Position

Professor

External Links

Career 【 Display / hide

  • 2004.04
    -
    2005.03

    日本学術振興会 特別研究員(DC2)

  • 2005.04
    -
    2008.03

    日本学術振興会 特別研究員(PD)

  • 2008.04
    -
    2011.03

    高知大学, 理学部, 助教

  • 2011.04
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    2013.03

    慶應義塾大学, 商学部, 専任講師

Academic Background 【 Display / hide

  • 2005.03

    Keio University, 理工学研究科, 基礎理工学

    Graduate School, Completed, Doctoral course

Academic Degrees 【 Display / hide

  • 博士(理学), Keio University, Coursework, 2005.03

 

Research Areas 【 Display / hide

  • Foundations of mathematics/Applied mathematics (General Mathematics (includes Probability Theory/Statistical Mathematics))

 

Papers 【 Display / hide

  • Induced Nets and Hamiltonicity of Claw-Free Graphs

    Chiba S., Fujisawa J.

    Graphs and Combinatorics (Graphs and Combinatorics)   2021

    ISSN  09110119

     View Summary

    The connected graph of degree sequence 3, 3, 3, 1, 1, 1 is called a net, and the vertices of degree 1 in a net are called its endvertices. Broersma conjectured in 1993 that a 2-connected graph G with no induced K1 , 3 is hamiltonian if every endvertex of each induced net of G has degree at least (| V(G) | - 2) / 3. In this paper we prove this conjecture in the affirmative.

  • Distance Matching Extension in Cubic Bipartite Graphs

    Aldred R.E.L., Fujisawa J., Saito A.

    Graphs and Combinatorics (Graphs and Combinatorics)   2021

    ISSN  09110119

     View Summary

    A graph G is said to be distanced matchable if, for any matching M of G in which edges are pairwise at least distance d apart, there exists a perfect matching M∗ of G which contains M. In this paper, we prove the following results: (i) if G is a cubic bipartite graph in which, for each e∈ E(G) , there exist two cycles C1, C2 of length at most d such that E(C1) ∩ E(C2) = { e} , then G is distance d- 1 matchable, and (ii) if G is a planar or projective planar cubic bipartite graph in which, for each e∈ E(G) , there exist two cycles C1, C2 of length at most 6 such that e∈ E(C1) ∩ E(C2) , then G is distance 6 matchable.

  • Non-hamiltonian 1-tough triangulations with disjoint separating triangles

    Fujisawa J., Zamfirescu C.T.

    Discrete Applied Mathematics (Discrete Applied Mathematics)  284   622 - 625 2020.09

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  0166218X

     View Summary

    In this note, we consider triangulations of the plane. Ozeki and the second author asked whether there are non-hamiltonian 1-tough triangulations in which every two separating triangles are disjoint. We answer this question in the affirmative and strengthen a result of Nishizeki by proving that there are infinitely many non-hamiltonian 1-tough triangulations with pairwise disjoint separating triangles.

  • Distance matching extension and local structure of graphs

    Aldred R., Fujisawa J., Saito A.

    Journal of Graph Theory (Journal of Graph Theory)  93 ( 1 ) 5 - 20 2020.01

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  03649024

     View Summary

    © 2019 Wiley Periodicals, Inc. A matching M in a graph G is said to be extendable if there exists a perfect matching of G containing M. Also, M is said to be a distance d matching if the shortest distance between a pair of edges in M is at least d. A graph G is distance d matchable if every distance d matching is extendable in G, regardless of its size. In this paper, we study the class of distance d matchable graphs. In particular, we prove that for every integer K with k ≥ 3, there exists a positive integer d such that every connected, locally (k − 1)-connected K1,k-free graph of even order is distance d matchable. We also prove that every connected, locally K-connected K1,f-free graph of even order is distance 3 matchable. Furthermore, we make more detailed analysis of K1,4-free graphs and study their distance matching extension properties.

  • Edge proximity and matching extension in projective planar graphs

    Fujisawa J., Seno H.

    Journal of Graph Theory (Journal of Graph Theory)  95 ( 3 ) 341 - 367 2020

    Research paper (scientific journal), Joint Work, Accepted,  ISSN  03649024

     View Summary

    © 2020 Wiley Periodicals, Inc. A graph G with at least 2m + 2 vertices is said to be distance d m-extendable if, for any matching M of G with m edges in which the edges lie at distance at least d pairwise, there exists a perfect matching of M containing M. In this paper we prove that every 5-connected triangulation on the projective plane of even order is distance 3 7-extendable and distance 3 7-extendable for any m.

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Papers, etc., Registered in KOARA 【 Display / hide

Presentations 【 Display / hide

  • A proof of Broersma's conjecture on Hamiltonicity of claw-free graphs

    千葉 周也,藤沢 潤

    2019.12, Oral Presentation(general)

  • ハミルトンサイクルを持たない 1-tough な三角形分割とその分離三角形

    藤沢 潤

    Japanese Conference on Combinatorics and its Applications (JCCA-2019), 2019.08, Oral Presentation(general)

  • ハミルトンサイクルを持たない1-tough な三角形分割とその分離三角形について

    藤沢 潤,C. T. Zamfirescu

    日本数学会 2019年度年会 (東京工業大学大岡山キャンパス) , 2019.03, Oral Presentation(general)

  • On distance matching extension in graphs

    J. Fujisawa

    2018 SCMS Workshop on Extremal and Structural Graph Theory (Shanghai, China) , 2018.12, Oral Presentation(guest/special)

  • 3-正則グラフにおけるdistance matchable なグラフのクラスについて

    藤沢 潤,R.E.L. Aldred,斎藤 明

    離散数学とその応用研究集会2018 (広島工業大学広島校舎) , 2018.08, Oral Presentation(general)

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Research Projects of Competitive Funds, etc. 【 Display / hide

  • グラフの距離拡張性を用いた因子問題の研究

    2020.04
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    2024.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 藤沢 潤, Grant-in-Aid for Scientific Research (C), Principal Investigator

  • 科学研究費補助金 (基盤研究C)

    2018.04
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    Present

  • 閉曲面上のグラフにおける因子問題の研究

    2017.04
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    2020.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 藤沢 潤, Grant-in-Aid for Scientific Research (C), Principal Investigator

  • 科学研究費補助金 (若手研究B)

    2014.04
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    2017.03

    Principal Investigator

  • On factor problems in graphs with high regularity

    2014.04
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    2017.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 藤沢 潤, Grant-in-Aid for Young Scientists (B), Principal Investigator

     View Summary

    The following is the main part of the results obtained in this research. Firstly, as for the problem of determining whether every 5-connected projective planar triangulation is distance d m-extendable or not, we solved the d=4 case. Secondly, in 5-connected planar graphs with at most two non-triangular faces, we obtained the best threshold on distance matching extendability, which was not shown in the former research. Thirdly, it turned out that highly locally-connected star free graphs of even order have the property such that every matching in which the edges lie pairwise distance far apart is extendable.

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Courses Taught 【 Display / hide

  • PRACTICES IN LINEAR ALGEBRA

    2021

  • INTERNSHIP

    2021

  • INTERMEDIATE LINEAR ALGEBRA

    2021

  • INDEPENDENT STUDY (INTERNATIONAL BUSINESS)

    2021

  • GENERAL EDUCATION SEMINAR (S)

    2021

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Memberships in Academic Societies 【 Display / hide

  • 日本数学会

     

Committee Experiences 【 Display / hide

  • 2016.10
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    2018.09

    応用数学分科会委員, 日本数学会