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STUDIES ON GRAPH FACTORS

Research Project

Project/Area Number 14540135
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionSHIBAURA INSTITUTE OF TECHNOLOGY

Principal Investigator

NISHIMURA Tsuyoshi  SHIBAURA INST. OF TECH, ENGINEERING, ASSISTANT PROFESSOR, 工学部, 助教授 (80237734)

Project Period (FY) 2002 – 2003
Project Status Completed (Fiscal Year 2003)
Budget Amount *help
¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 2003: ¥1,200,000 (Direct Cost: ¥1,200,000)
Fiscal Year 2002: ¥1,500,000 (Direct Cost: ¥1,500,000)
Keywords1-FACTORS / FACTOR-CRITICALITY / EXTENDABILITY / COMPLETE-FACTORS / NUMBER OF COMPONENTS / LOCAALLY CONNECTED / CLOSURE / ノー因子 / 完全-因子 / Complete-factor / factor-critical / extendable / perfect matching / 1-factors / claw-free / 2-factors
Research Abstract

Firstly, we treated a study of a relation between complete-factors and matching extension. In this study, we had the following result.
Let k and p be nonnegative integers with k≡p (mod 2). Let G be a graph of order p, F a complete-factor of G satisfying the connectivity k(G) > k or the component number w(G) > 2. For any component C of F, let C' =C or C-{v} according as p-lC'l≡ k (mod 2) or p-lCl≡ k-1 (mod 2), where v is some fixed vertex in C. If G-C' is k-factor-critical for all C∈ F, then G is k-factor-critical. We also proved a several results for this topic.
We proved the following theorem: Let G be a graph and let x be a locally 2n-connected vertex. Let {u,v} be a pair of vertices in V(G)-{x} such that uv 【not a member of】E(G), x ∈ N (u) ∩ N (v), and N (x) ⊂ N(u) ∪ N (v)∪{u,v}. Then if G+uv is n-extendable, then G is n-extendable or G is a member of the exceptional family F of graphs.
And also we proved that, for (2n+1)-connected graphs, we have the same conclusion under the same neighborhood condition and deletion of locally connected condition.

Report

(3 results)
  • 2003 Annual Research Report   Final Research Report Summary
  • 2002 Annual Research Report
  • Research Products

    (1 results)

All Other

All Publications (1 results)

  • [Publications] TSUYOSHI NISHIMURA: "A closure concept in factor-critical graphs"Discrete Mathematics. 259. 319-324 (2002)

    • Related Report
      2002 Annual Research Report

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Published: 2002-04-01   Modified: 2016-04-21  

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