Updated on 2025/04/13

写真a

 
KITA Nanao
 
Organization
Graduate School of Mathematics Division of Mathematics Computational Mathematics Associate professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Associate professor
External link

Degree 3

  1. PhD in Science ( 2014.3   Keio University ) 

  2. Master of Information Science and Technology ( 2011.3   The University of Tokyo ) 

  3. Bachelor of Engineering ( 2008.3   The University of Tokyo ) 

Research Interests 4

  1. Discrete Mathematics

  2. Theoretical Computer Science

  3. Graph Theory

  4. Optimization Theory

Research Areas 2

  1. Informatics / Mathematical informatics

  2. Informatics / Theory of informatics

Committee Memberships 2

  1. The Mathematical Society of Japan   delegate  

    2024.3 - 2025.2   

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    Committee type:Academic society

  2. The 37th International Conference on Formal Power Series and Algebraic Combinatorics   Organizing Committee  

    2023.7   

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    Committee type:Academic society

Awards 1

  1. Best Student Paper Award

    2012.12   23rd International Symposium on Algorithm and Computation (ISAAC 2012)  

    Nanao Kita

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    Award type:Award from international society, conference, symposium, etc.  Country:Taiwan, Province of China

 

Papers 5

  1. Odd cuts in bipartite grafts II: Structure and universality of decapital distance components

    Nanao Kita

    arXiv preprint   Vol. arXiv:2503.23973   2025.3

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    Authorship:Lead author, Corresponding author   Language:English   Publishing type:Research paper (bulletin of university, research institution)  

  2. Basilica: New canonical decomposition in matching theory Reviewed Open Access

    JOURNAL OF GRAPH THEORY   Vol. 108 ( 3 ) page: 508 - 542   2025.3

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    Authorship:Lead author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)   Publisher:Journal of Graph Theory  

    In matching theory, one of the most fundamental and classical branches of combinatorics, canonical decompositions of graphs are powerful and versatile tools that form the basis of this theory. However, the abilities of the known canonical decompositions, that is, the Dulmage–Mendelsohn, Kotzig–Lovász, and Gallai–Edmonds decompositions, are limited because they are only applicable to particular classes of graphs, such as bipartite graphs, or they are too sparse to provide sufficient information. To overcome these limitations, we introduce a new canonical decomposition that is applicable to all graphs and provides much finer information. This decomposition also provides the answer to the longstanding absence of a canonical decomposition that is nontrivially applicable to general graphs with perfect matchings. We focus on the notion of factor-components as the fundamental building blocks of a graph; through the factor-components, our new canonical decomposition states how a graph is organized and how it contains all the maximum matchings. The main results that constitute our new theory are the following: (i) a canonical partial order over the set of factor-components, which describes how a graph is constructed from its factor-components; (ii) a generalization of the Kotzig–Lovász decomposition, which shows the inner structure of each factor-component in the context of the entire graph; and (iii) a canonically described interrelationship between (i) and (ii), which integrates these two results into a unified theory of a canonical decomposition. These results are obtained in a self-contained way, and our proof of the generalized Kotzig–Lovász decomposition contains a shortened and self-contained proof of the classical counterpart.

    DOI: 10.1002/jgt.23190

    Open Access

    Web of Science

    Scopus

  3. Graft analogue of general Kotzig-Lovasz decomposition Reviewed

    Nanao Kita

    Discrete Applied Mathematics   Vol. 32 ( 2 ) page: 355 - 364   2022.12

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (scientific journal)  

    DOI: https://doi.org/10.1016/j.dam.2022.08.024

  4. Constructive characterization for signed analogue of critical graphs II: General radials and semiradials

    Nanao Kita

    arXiv     2022.6

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (bulletin of university, research institution)  

  5. Tight cuts in bipartite grafts I: Capital distance components

    Nanao Kita

    arXiv     2022.2

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    Authorship:Lead author, Last author, Corresponding author   Language:English   Publishing type:Research paper (bulletin of university, research institution)  

Presentations 1

  1. Dulmage--Mendelsohn Decomposition for the Minimum Odd Join Problem in Bipartite Grafts International conference

    Nanao Kita

    56th Southeastern International Conference on Combinatorics, Graph Theory & Computing (SEICCGTC)  2025.3.5 

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    Event date: 2025.3

    Language:English   Presentation type:Oral presentation (general)  

    Venue:Boca Raton, FL  

KAKENHI (Grants-in-Aid for Scientific Research) 2

  1. Innovating the foundation of Ising spin glass theory by an approach from discrete mathematics

    Grant number:23K03192  2023.4 - 2027.3

    Grants-in-Aid for Scientific Research  Grant-in-Aid for Scientific Research (C)

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    Authorship:Principal investigator 

    Grant amount:\4680000 ( Direct Cost: \3600000 、 Indirect Cost:\1080000 )

  2. マトロイダル最適化理論の抜本的拡張

    Grant number: 18K13451  2018.4 - 2024.3

    若手研究

    喜多 奈々緒

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    Authorship:Principal investigator  Grant type:Competitive

    Grant amount:\4160000 ( Direct Cost: \3200000 、 Indirect Cost:\960000 )