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 |
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Pages (from-to) | 3636-3642 |
Number of pages | 7 |
Journal | Discrete Mathematics |
Volume | 312 |
Issue number | 24 |
DOIs | |
Publication status | Published - 28 Dec 2012 |
Externally published | Yes |
Keywords
- Distance
- Planar
- Radius
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics