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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages70-78
Number of pages9
Volume4381 LNCS
DOIs
Publication statusPublished - 2007
Externally publishedYes
Event7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005 - Xi'an
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)03029743
ISSN (Electronic)16113349

Other

Other7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005
CityXi'an
Period05/11/2205/11/24

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Keywords

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

ASJC Scopus subject areas

  • Computer Science(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Theoretical Computer Science

Cite this

Kano, M., & Matsuda, H. (2007). A Neighborhood Condition for Graphs to Have [a, b]-Factors III. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 4381 LNCS, 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