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Some remarks on domination

✍ Scribed by D. Archdeacon; J. Ellis-Monaghan; D. Fisher; D. Froncek; P.C.B. Lam; S. Seager; B. Wei; R. Yuster

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 49 KB
Volume: 46
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20000

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

We prove a conjecture of Favaron et al. that every graph of order n and minimum degree at least three has a total dominating set of size at least n/2. We also present several related results about: (1) extentions to graphs of minimum degree two, (2) examining graphs where the bound is tight, and (3) a type of bipartite domination and its relation to transversals in hypergraphs. © 2004 Wiley Periodicals, Inc. J Graph Theory 46: 207–210, 2004

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