The radius of k-connected planar graphs with bounded faces

Patrick Ali; Peter Dankelmann; Simon Mukwembi

doi:10.1016/j.disc.2012.08.019

The radius of k-connected planar graphs with bounded faces

Patrick Ali, Peter Dankelmann, Simon Mukwembi

University of KwaZulu-Natal

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

9 Citations (Scopus)

Abstract

We prove that if G is a 3-connected plane graph of order p, maximum face length l and radius rad(G), then the bound rad(G)≤p6+5l6+23 holds. For constant l, our bound is shown to be asymptotically sharp and improves on a bound by Harant (1990) [6]. Furthermore we extend these results to 4- and 5-connected planar graphs.

Original language	English
Pages (from-to)	3636-3642
Number of pages	7
Journal	Discrete Mathematics
Volume	312
Issue number	24
DOIs	https://doi.org/10.1016/j.disc.2012.08.019
Publication status	Published - 28 Dec 2012
Externally published	Yes

Keywords

Distance
Planar
Radius

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

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10.1016/j.disc.2012.08.019

Cite this

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title = "The radius of k-connected planar graphs with bounded faces",

abstract = "We prove that if G is a 3-connected plane graph of order p, maximum face length l and radius rad(G), then the bound rad(G)≤p6+5l6+23 holds. For constant l, our bound is shown to be asymptotically sharp and improves on a bound by Harant (1990) [6]. Furthermore we extend these results to 4- and 5-connected planar graphs.",

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AU - Dankelmann, Peter

AU - Mukwembi, Simon

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Y1 - 2012/12/28

N2 - We prove that if G is a 3-connected plane graph of order p, maximum face length l and radius rad(G), then the bound rad(G)≤p6+5l6+23 holds. For constant l, our bound is shown to be asymptotically sharp and improves on a bound by Harant (1990) [6]. Furthermore we extend these results to 4- and 5-connected planar graphs.

AB - We prove that if G is a 3-connected plane graph of order p, maximum face length l and radius rad(G), then the bound rad(G)≤p6+5l6+23 holds. For constant l, our bound is shown to be asymptotically sharp and improves on a bound by Harant (1990) [6]. Furthermore we extend these results to 4- and 5-connected planar graphs.

KW - Distance

KW - Planar

KW - Radius

UR - https://www.scopus.com/pages/publications/84867099469

U2 - 10.1016/j.disc.2012.08.019

DO - 10.1016/j.disc.2012.08.019

M3 - Article

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SN - 0012-365X

VL - 312

SP - 3636

EP - 3642

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 24

ER -

The radius of k-connected planar graphs with bounded faces

Abstract

Keywords

ASJC Scopus subject areas

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