An upper bound on the domination number of n-vertex connected cubic graphs

A. V. Kostochka; B. Y. Stodolsky

doi:10.1016/j.disc.2007.12.009

An upper bound on the domination number of n-vertex connected cubic graphs

A. V. Kostochka^*, B. Y. Stodolsky

^*Corresponding author for this work

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

20 Citations (Scopus)

Abstract

In 1996, Reed proved that the domination number γ (G) of every n-vertex graph G with minimum degree at least 3 is at most 3 n / 8. This bound is sharp for cubic graphs if there is no restriction on connectivity. In this paper we show that γ (G) ≤ 4 n / 11 for every n-vertex cubic connected graph G if n > 8. Note that Reed's conjecture that γ (G) ≤ ⌈ n / 3 ⌉ for every connected cubic n-vertex graph G is not true.

Original language	English
Pages (from-to)	1142-1162
Number of pages	21
Journal	Discrete Mathematics
Volume	309
Issue number	5
DOIs	https://doi.org/10.1016/j.disc.2007.12.009
Publication status	Published - 28 Mar 2009
Externally published	Yes

Keywords

Connected graphs
Cubic graphs
Domination

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10.1016/j.disc.2007.12.009

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abstract = "In 1996, Reed proved that the domination number γ (G) of every n-vertex graph G with minimum degree at least 3 is at most 3 n / 8. This bound is sharp for cubic graphs if there is no restriction on connectivity. In this paper we show that γ (G) ≤ 4 n / 11 for every n-vertex cubic connected graph G if n > 8. Note that Reed's conjecture that γ (G) ≤ ⌈ n / 3 ⌉ for every connected cubic n-vertex graph G is not true.",

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author = "Kostochka, {A. V.} and Stodolsky, {B. Y.}",

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AU - Stodolsky, B. Y.

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N2 - In 1996, Reed proved that the domination number γ (G) of every n-vertex graph G with minimum degree at least 3 is at most 3 n / 8. This bound is sharp for cubic graphs if there is no restriction on connectivity. In this paper we show that γ (G) ≤ 4 n / 11 for every n-vertex cubic connected graph G if n > 8. Note that Reed's conjecture that γ (G) ≤ ⌈ n / 3 ⌉ for every connected cubic n-vertex graph G is not true.

AB - In 1996, Reed proved that the domination number γ (G) of every n-vertex graph G with minimum degree at least 3 is at most 3 n / 8. This bound is sharp for cubic graphs if there is no restriction on connectivity. In this paper we show that γ (G) ≤ 4 n / 11 for every n-vertex cubic connected graph G if n > 8. Note that Reed's conjecture that γ (G) ≤ ⌈ n / 3 ⌉ for every connected cubic n-vertex graph G is not true.

KW - Connected graphs

KW - Cubic graphs

KW - Domination

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JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 5

ER -

An upper bound on the domination number of n-vertex connected cubic graphs

Abstract

Keywords

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