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A linear vizing-like relation between the size and the domination number of a graph

✍ Scribed by Rautenbach, Dieter

Publisher: John Wiley and Sons
Year: 1999
Tongue: English
Weight: 174 KB
Volume: 31
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199908)31:4<297::aid-jgt4>3.0.co;2-1

No coin nor oath required. For personal study only.

✦ Synopsis

We prove m ≤ ∆n -(∆ + 1)γ for every graph without isolated vertices of order n, size m, domination number γ and maximum degree ∆ ≥ 3.

This generalizes a result of Fisher et al., CU-Denver Tech Rep, 1996] who obtained the given bound for the case ∆ = 3.

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