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From L. Euler to D. König

Published online by Cambridge University Press:  22 July 2009

Dominique de Werra
Dominique de Werra*
Affiliation:
École Polytechnique Fédérale de Lausanne (Switzerland); dominique.dewerra@epfl.ch
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Abstract

Starting from the famous Königsberg bridge problem which Euler described in 1736, we intend to show that some results obtained 180 years later by König are very close to Euler's discoveries.

Keywords

Eulerian graphedge coloringparityKönig theorem.
Type
Research Article
Information
RAIRO - Operations Research , Volume 43 , Issue 3: ROADEF 06 , July 2009 , pp. 247 - 251
Copyright
© EDP Sciences, ROADEF, SMAI, 2009

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References

C. Berge, Graphes. Gauthier-Villars, Paris (1983).
D. de Werra, Equitable colorations of graphs. Revue Française d'Informatique et de Recherche Opérationnelle R-3 (1971) 3–8.
L. Euler, Solutio problematis ad geometriam situs pertinentis, Commentarii Academiae Scientiarum Imperialis Petropolitanae 8 (1736) 128–140. Reprinted in: Leonhardi Euleri – Opera Omnia – Series Prima – Opera Mathematica – Commentationes Algebraicae, L.G. du Pasquier Ed., Teubner, Leipzig (1923) 1–10.
Gabow, H.N., Using Euler partitions to edge color bipartite multigraphs. Int. J. Parallel Prog. 5 (1976) 345–355.
Gribkovskai, I., Halskan, Ø. and Laporte, G., The bridges of Königsberg – a historical perspective. Networks 49 (2007) 199–203. CrossRef
Hierholzer, C., Über die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren. Math. Ann. 6 (1873) 30–32. CrossRef
König, D., Graphok és alkalmazásuk a determinánsok és a halmazok elméletére (Hungarian). Mathematikai és Természettudományi Értesitö 34 (1916) 104–119.
Schrijver, A., Bipartite edge coloring in $0(\delta m) \mbox{time}$ . SIAM J. Comput. 28 (1998) 841–846. CrossRef