On domination in 2-connected cubic graphs

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On domination in 2-connected cubic graphs

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by B. Y. Stodolsky

BibTeX

@MISC{Stodolsky_ondomination,
    author = {B. Y. Stodolsky},
    title = {On domination in 2-connected cubic graphs},
    year = {}
}

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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 3n/8 and conjectured that γ(H) ≤ ⌈n/3 ⌉ for every connected 3-regular (cubic) n-vertex graph H. In [1] this conjecture was disproved by presenting a connected cubic graph G on 60 vertices with γ(G) = 21 and a sequence {Gk} ∞ k=1 of connected cubic graphs with limk→∞ γ(Gk) |V (Gk)|

Keyphrases

2-connected cubic graph n-vertex graph cubic graph sequence gk domination number minimum degree

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