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Topological circles and Euler tours in locally finite graphs
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Georgakopoulos, Agelos (2008) Topological circles and Euler tours in locally finite graphs. The Electronic Journal of Combinatorics, Vol.16 . Article no. R40. ISSN 2150-959X.
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Official URL: http://www.combinatorics.org/ojs/index.php/eljc/ar...
Abstract
We obtain three results concerning topological paths ands circles in the end compactification |G| of a locally finite connected graph G. Confirming a conjecture of Diestel we show that through every edge set E∈C there is a topological Euler tour, a continuous map from the circle S1 to the end compactification |G| of G that traverses every edge in E exactly once and traverses no other edge.
Second, we show that for every sequence (τi)i∈N of topological x–y paths in |G| there is a topological x–y path in |G| all of whose edges lie eventually in every member of some fixed subsequence of (τi). It is pointed out that this simple fact has several applications some of which reach out of the realm of |G|.
Third, we show that every set of edges not containing a finite odd cut of G extends to an element of C.
Item Type: | Journal Article | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||
Journal or Publication Title: | The Electronic Journal of Combinatorics | ||||
Publisher: | Electronic Journal of Combinatorics | ||||
ISSN: | 2150-959X | ||||
Official Date: | 2008 | ||||
Dates: |
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Volume: | Vol.16 | ||||
Page Range: | Article no. R40 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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