Fujisawa, Jun

写真a

Affiliation

Faculty of Business and Commerce (Hiyoshi)

Position

Professor

External Links
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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
    -
    2013.03

    慶應義塾大学, 商学部, 専任講師

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Academic Background 【 Display / hide 】

  • 2003.04
    -
    2005.03

    Keio University, 理工学研究科, 基礎理工学専攻後期博士課程

    Graduate School, Completed, Doctoral course

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Academic Degrees 【 Display / hide 】

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

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Research Areas 【 Display / hide 】

  • Natural Science / Basic mathematics (General Mathematics (includes Probability Theory/Statistical Mathematics))

  • Natural Science / Applied mathematics and statistics (General Mathematics (includes Probability Theory/Statistical Mathematics))

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Papers 【 Display / hide 】

  • Resonant hexagons in fullerene graphs

    Fujisawa J.

    Journal of Mathematical Chemistry 62 ( 9 ) 2280 - 2288 2024.10

    ISSN  02599791

    　View Summary

    A fullerene graph is a 3-connected plane cubic graph in which every face is pentagonal or hexagonal. A set of hexagons H of G is called a resonant pattern if there exists a perfect matching M of G such that exactly three edges of H is contained in M for each member H of H. In this paper we prove for any natural number k that almost all of the family of k disjoint hexagons are resonant patterns in sufficiently large fullerene graphs.

  • Hamilton cycles passing through a matching in a bipartite graph with high degree sum

    Fujisawa J., Tsugaki M., Yamashita T., Yashima T.

    Discrete Mathematics (Discrete Mathematics)  347 ( 1 )  2024.01

    ISSN  0012365X

    　View Summary

    Let G be a balanced bipartite graph of order 2n with partite sets X and Y, and M be a matching of k edges in G. Let σ1,1(G)=min⁡{dG(x)+dG(y):x∈X,y∈Y,xy∉E(G)}. Conditions on σ1,1(G) for the existence of a Hamilton cycle passing through M have been studied by many researchers, but the threshold is not known to be sharp for [Formula presented]. In this paper we prove that G has a Hamilton cycle passing through all the edges of M if σ1,1(G)≥2n−k and k≤n−2. Moreover, we show that the lower bound on σ1,1(G) is sharp for every k with [Formula presented].

  • Removal of subgraphs and perfect matchings in graphs on surfaces

    Aldred R.E.L., Fujisawa J.

    Journal of Graph Theory (Journal of Graph Theory)  102 ( 2 ) 304 - 321 2023.02

    ISSN  03649024

    　View Summary

    Let (Formula presented.) be the Euler characteristic of a surface (Formula presented.). We characterize the set of graphs (Formula presented.) of order at most 6 which satisfies the following: If (Formula presented.) is a 5-connected graph embedded in a surface (Formula presented.) of face-width at least (Formula presented.) and (Formula presented.) is a subgraph of (Formula presented.) isomorphic to (Formula presented.) such that (Formula presented.) has even order, then (Formula presented.) has a perfect matching. An analogous result on near-perfect matching is given as well. Moreover, we show the following result. Let (Formula presented.) be a 5-connected graph embedded in a surface (Formula presented.) and let (Formula presented.) be connected subgraphs of (Formula presented.) of size at most (Formula presented.) which lie pairwise sufficiently far apart in the face-subdivision of (Formula presented.). We prove that, if the face-width of (Formula presented.) is at least (Formula presented.) and (Formula presented.) satisfies (Formula presented.) for each (Formula presented.) with (Formula presented.), then (Formula presented.) satisfies (Formula presented.) as well, where (Formula presented.) is said to satisfy (Formula presented.) if (Formula presented.) has at most (Formula presented.) components for every (Formula presented.). It is also shown that the distance condition can be considerably weakened when (Formula presented.) triangulates the surface. All of these results generalize previous studies on matching extension in graphs on surfaces.

  • Game chromatic number of strong product graphs

    Enomoto H., Fujisawa J., Matsumoto N.

    Discrete Mathematics (Discrete Mathematics)  346 ( 1 )  2023.01

    ISSN  0012365X

    　View Summary

    The graph coloring game is a two-player game in which the two players properly color an uncolored vertex of G alternately. The first player wins the game if all vertices of G are colored, and the second wins otherwise. The game chromatic number of a graph G is the minimum integer k such that the first player has a winning strategy for the graph coloring game on G with k colors. There is a lot of literature on the game chromatic number of graph products, e.g., the Cartesian product and the lexicographic product. In this paper, we investigate the game chromatic number of the strong product of graphs, which is one of major graph products. In particular, we completely determine the game chromatic number of the strong product of a double star and a complete graph. Moreover, we estimate the game chromatic number of some King's graphs, which are the strong products of two paths.

  • Induced Nets and Hamiltonicity of Claw-Free Graphs

    Chiba S., Fujisawa J.

    Graphs and Combinatorics (Graphs and Combinatorics)  37 ( 3 ) 663 - 690 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.

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

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Presentations 【 Display / hide 】

  • Recent progress on distance matching extension in graphs on surfaces

    Jun Fujisawa

    The 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023), 

    2023.08
    , 

    Oral presentation (invited, special)

  • Removal of subgraphs and perfect matchings in graphs on surfaces

    Jun Fujisawa

    2023 Montreal Graph Theory Workshop, 

    2023.05
    , 

    Oral presentation (invited, special)

  • 閉曲面上の三角形分割でない5-連結グラフにおけるマッチング拡張問題

    R.E.L. Aldred, 藤沢 潤

    日本数学会 2023年度年会, 

    2023.03
    , 

    Oral presentation (general)

  • 閉曲面上のグラフにおける部分グラフの除去と完全マッチングの存在について

    藤沢 潤

    第33回位相幾何学的グラフ理論研究集会, 

    2021.11
    , 

    Oral presentation (general)

  • 閉曲面上のグラフにおける距離が離れたマッチングの拡張問題とその一般化

    R.E.L. Aldred, 藤沢 潤

    日本数学会 2021年度秋季総合分科会, 

    2021.09
    , 

    Oral presentation (general)

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

  • グラフの2部性に着目した因子問題の研究

    2024.04
    -
    2028.03

    基盤研究(C), Principal investigator

  • グラフの距離拡張性を用いた因子問題の研究

    2020.04
    -
    2024.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Principal investigator

  • 閉曲面上のグラフにおける因子問題の研究

    2017.04
    -
    2020.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Principal investigator

  • On factor problems in graphs with high regularity

    2014.04
    -
    2017.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, 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.

  • 科学研究費補助金 (若手研究B)

    2010.04
    -
    2014.03

    No Setting

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Courses Taught 【 Display / hide 】

  • PRACTICES IN LINEAR ALGEBRA

    2025

  • INTERMEDIATE LINEAR ALGEBRA

    2025

  • GENERAL EDUCATION SEMINAR (S)

    2025

  • CALCULUS 1

    2025

  • BASIC THEORY OF GAMES

    2025

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Memberships in Academic Societies 【 Display / hide 】

  • 日本数学会

    　
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Committee Experiences 【 Display / hide 】

  • 2016.10
    -
    2018.09

    応用数学分科会委員, 日本数学会

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