Open packing, total domination, and the P3-Radon number

Michael A. Henning; Dieter Rautenbach; Philipp M. Schäfer

doi:10.1016/j.disc.2013.01.022

Open packing, total domination, and the P₃-Radon number

Michael A. Henning, Dieter Rautenbach, Philipp M. Schäfer

Mathematics and Applied Mathematics

Ulm University

Research output: Contribution to journal › Article › peer-review

9 Citations (Scopus)

Abstract

Let r(G), ρ_o(G), and γ_t(G) denote the P₃-Radon number, the open packing number, and the total domination number of a graph G. We prove that r(T)≤2ρ_o(T)+1 for every tree T and r(G)<2γ_t(G)+1 for every non-trivial regular graph G.

Original language	English
Pages (from-to)	992-998
Number of pages	7
Journal	Discrete Mathematics
Volume	313
Issue number	9
DOIs	https://doi.org/10.1016/j.disc.2013.01.022
Publication status	Published - 2013

Keywords

Graph convexity
Open packing
Radon number
Radon partition
Total domination

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.disc.2013.01.022

Cite this

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title = "Open packing, total domination, and the P3-Radon number",

abstract = "Let r(G), ρo(G), and γt(G) denote the P3-Radon number, the open packing number, and the total domination number of a graph G. We prove that r(T)≤2ρo(T)+1 for every tree T and r(G)<2γt(G)+1 for every non-trivial regular graph G.",

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AU - Henning, Michael A.

AU - Rautenbach, Dieter

AU - Schäfer, Philipp M.

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N2 - Let r(G), ρo(G), and γt(G) denote the P3-Radon number, the open packing number, and the total domination number of a graph G. We prove that r(T)≤2ρo(T)+1 for every tree T and r(G)<2γt(G)+1 for every non-trivial regular graph G.

AB - Let r(G), ρo(G), and γt(G) denote the P3-Radon number, the open packing number, and the total domination number of a graph G. We prove that r(T)≤2ρo(T)+1 for every tree T and r(G)<2γt(G)+1 for every non-trivial regular graph G.

KW - Graph convexity

KW - Open packing

KW - Radon number

KW - Radon partition

KW - Total domination

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