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

M. Kano; Haruhide Matsuda

doi:10.1007/978-3-540-70666-3_8

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

M. Kano, Haruhide Matsuda

Research output: Chapter in Book/Report/Conference proceeding › Conference 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 (x_k )| ≥ 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 language	English
Title of host publication	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
Pages	70-78
Number of pages	9
DOIs	https://doi.org/10.1007/978-3-540-70666-3_8
Publication status	Published - 2007
Externally published	Yes
Event	7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005 - Xi'an, China Duration: 2005 Nov 22 → 2005 Nov 24

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	4381 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005
Country/Territory	China
City	Xi'an
Period	05/11/22 → 05/11/24

Keywords

Factor
Neighborhood union
[a, b]-factor

ASJC Scopus subject areas

Theoretical Computer Science
Computer Science(all)

Access to Document

10.1007/978-3-540-70666-3_8

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

A Neighborhood Condition for Graphs to Have [a, b]-Factors III. / Kano, M.; Matsuda, Haruhide.

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. 2007. p. 70-78 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 4381 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 4381 LNCS, pp. 70-78, 7th China-Japan Conference on Discrete Geometry, Combinatorics and Graph Theory, CJCDGCGT 2005, Xi'an, China, 05/11/22. https://doi.org/10.1007/978-3-540-70666-3_8

Kano M, Matsuda H. 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. 2007. p. 70-78. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-70666-3_8

Kano, M. ; Matsuda, Haruhide. / A Neighborhood Condition for Graphs to Have [a, b]-Factors III. 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. 2007. pp. 70-78 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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author = "M. Kano and Haruhide Matsuda",

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N2 - 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).

AB - 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).

KW - Factor

KW - Neighborhood union

KW - [a, b]-factor

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

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