{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T18:00:46Z","timestamp":1775844046776,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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 $E\\in {\\cal C}$ there is a topological Euler tour, a continuous map from the circle $S^1$ 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 $(\\tau_i)_{i\\in \\Bbb N}$ of topological $x$\u2013$y$ paths in $|G|$ there is a topological $x$\u2013$y$ path in $|G|$ all of whose edges lie eventually in every member of some fixed subsequence of $(\\tau_i)$. 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 $\\cal C$.<\/jats:p>","DOI":"10.37236\/129","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:32:42Z","timestamp":1578699162000},"source":"Crossref","is-referenced-by-count":6,"title":["Topological Circles and Euler Tours in Locally Finite Graphs"],"prefix":"10.37236","volume":"16","author":[{"given":"Agelos","family":"Georgakopoulos","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,3,25]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r40\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:05:11Z","timestamp":1579298711000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3,25]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/129","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,3,25]]},"article-number":"R40"}}