On general frameworks and threshold functions for multiple domination

Zverovich, Vadim

Abstract

© 2015 Elsevier B.V. All rights reserved. We consider two general frameworks for multiple domination, which are called (r,s)-domination and parametric domination. They generalise and unify {k}-domination, k-domination, total k-domination and k-tuple domination. In this paper, known upper bounds for the classical domination are generalised for the (r,s)-domination and parametric domination numbers. These generalisations are based on the probabilistic method and they imply new upper bounds for the {k}-domination and total k-domination numbers. Also, we study threshold functions, which impose additional restrictions on the minimum vertex degree, and present new upper bounds for the aforementioned numbers. Those bounds extend similar known results for k-tuple domination and total k-domination.

• Journal Article Type: Article
• Publication Date: Jun 8, 2015
• Deposit Date: Jun 2, 2015
• Publicly Available Date: Jun 6, 2016
• Journal: Discrete Mathematics
• Print ISSN: 0012-365X
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 338
• Issue: 11
• Pages: 2095-2104
• DOI: https://doi.org/10.1016/j.disc.2015.05.003
• Keywords: -domination, parametric domination, {k}-domination, k-domination, total k-domination, k-tuple domination, upper bounds, threshold functions
• Public URL: https://uwe-repository.worktribe.com/output/803594
• Publisher URL: http://dx.doi.org/10.1016/j.disc.2015.05.003
• Related Public URLs: http://www.sciencedirect.com/science/journal/aip/0012365X
• Contract Date: Feb 26, 2016