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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
David J. Aldous
Department of Statistics 367 Evans Hall #3860 U.C. Berkeley CA 94720 USA
Electrical & Electronics Engineering

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Routed planar networks David J. Aldous
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 4, No 1 (2016): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2016.4.1.5

Abstract

Modeling a road network as a planar graph seems very natural. However, in studying continuum limits of such networks it is useful to take {\em routes} rather than {\em edges} as primitives. This article is intended to introduce the relevant (discrete setting) notion of {\em routed network} to graph theorists. We give a naive classification of all 71 topologically different such networks on 4 leaves, and pose a variety of challenging research questions.
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