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Erratum to: “A linear vizing-like relation relating the size and total domination number of a graph”

✍ Scribed by Erfang Shan; Liying Kang; Michael A. Henning

Publisher: John Wiley and Sons
Year: 2007
Tongue: English
Weight: 83 KB
Volume: 54
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20223

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✦ Synopsis

Abstract

The proof of the main theorem in the paper [1] is incorrect as it is missing an important case. Here we complete the proof by giving the missing case. © 2007 Wiley Periodicals, Inc. J Graph Theory 54: 350–353, 2007

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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.