A neighborhood condition for graphs to have [a, b]-factors

Haruhide Matsuda

doi:10.1016/S0012-365X(00)00140-0

A neighborhood condition for graphs to have [a, b]-factors

Haruhide Matsuda

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

Let G be a graph of order n, and let a and b be integers such that 1 ≤ a < b. Then we prove that G has an [a, b]-factor if the minimum degree δ(G) ≥ a, n ≥ 2(a + b)(a + b - 1)/b and |N_G(X) ∪ N_G(y)| ≥ an/(a + b) for any two non-adjacent vertices x and y of G. This result is best possible in some sense and it is an extension of the result of Li and Cai (A degree condition for a graph to have [a, b]-factors, J. Graph Theory 27 (1998) 1-6).

Original language	English
Pages (from-to)	289-292
Number of pages	4
Journal	Discrete Mathematics
Volume	224
Issue number	1-3
DOIs	https://doi.org/10.1016/S0012-365X(00)00140-0
Publication status	Published - 2000 Sep 28
Externally published	Yes

Keywords

Factor
Graph
Neighborhood
[a, b]-factor

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/S0012-365X(00)00140-0

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AB - Let G be a graph of order n, and let a and b be integers such that 1 ≤ a < b. Then we prove that G has an [a, b]-factor if the minimum degree δ(G) ≥ a, n ≥ 2(a + b)(a + b - 1)/b and |NG(X) ∪ NG(y)| ≥ an/(a + b) for any two non-adjacent vertices x and y of G. This result is best possible in some sense and it is an extension of the result of Li and Cai (A degree condition for a graph to have [a, b]-factors, J. Graph Theory 27 (1998) 1-6).

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KW - Neighborhood

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