A Neighborhood Condition for Graphs to Have [a, b]-Factors III

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

Let a, b, k, and m be positive integers such that 1 ≤a < b and 2 k (b + 1 - m)/a. Let G = (V(G), E(G)) be a graph of order |G|. Suppose that |G| > (a + b)(k(a + b - 1) - 1)/b and |N G (x 1) ∪ N G (x 2)... ∪ N G (xk )| ≥ a|G|/(a + b) for every independent set { x 1, x 2, ..., x k} ⊆ V(G). Then for any subgraph H of G with m edges and δ(G - E(H))≥ a, G has an [a, b]-factor F such that E(H)∩ E(F) = θ. This result is best possible in some sense and it is an extension of the result of Matsuda (Discrete Mathematics 224 (2000) 289-292).

Original languageEnglish
Title of host publicationDiscrete Geometry, Combinatorics and Graph Theory 7th China-Japan Conference, CJCDGCGT 2005, Tianjin, China, November 18-20, 2005, Xi'an, China, November 22-24, 2005, Revised Selected Papers
Pages70-78
Number of pages9
DOIs
Publication statusPublished - 2007 Dec 1
Externally publishedYes
Event7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005 - Xi'an, China
Duration: 2005 Nov 222005 Nov 24

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume4381 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005
CountryChina
CityXi'an
Period05/11/2205/11/24

Keywords

  • Factor
  • Neighborhood union
  • [a, b]-factor

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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  • Cite this

    Kano, M., & Matsuda, H. (2007). A Neighborhood Condition for Graphs to Have [a, b]-Factors III. In Discrete Geometry, Combinatorics and Graph Theory 7th China-Japan Conference, CJCDGCGT 2005, Tianjin, China, November 18-20, 2005, Xi'an, China, November 22-24, 2005, Revised Selected Papers (pp. 70-78). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4381 LNCS). https://doi.org/10.1007/978-3-540-70666-3_8