From L. Euler to D. König
RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 3, pp. 247-251.

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.

DOI : 10.1051/ro/2009020
Classification : 05C15
Mots-clés : eulerian graph, edge coloring, parity, König theorem 
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Werra, Dominique de. From L. Euler to D. König. RAIRO - Operations Research - Recherche Opérationnelle, Tome 43 (2009) no. 3, pp. 247-251. doi : 10.1051/ro/2009020. http://www.numdam.org/articles/10.1051/ro/2009020/

[1] C. Berge, Graphes. Gauthier-Villars, Paris (1983). | MR | Zbl

[2] D. De Werra, Equitable colorations of graphs. Revue Française d'Informatique et de Recherche Opérationnelle R-3 (1971) 3-8. | Numdam | MR | Zbl

[3] 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.

[4] H.N. Gabow, Using Euler partitions to edge color bipartite multigraphs. Int. J. Parallel Prog. 5 (1976) 345-355. | MR | Zbl

[5] I. Gribkovskai, Ø. Halskan and G. Laporte, The bridges of Königsberg - a historical perspective. Networks 49 (2007) 199-203. | MR | Zbl

[6] C. Hierholzer, Über die Möglichkeit, einen Linienzug ohne Wiederholung und ohne Unterbrechung zu umfahren. Math. Ann. 6 (1873) 30-32. | JFM | MR

[7] D. König, Graphok és alkalmazásuk a determinánsok és a halmazok elméletére (Hungarian). Mathematikai és Természettudományi Értesitö 34 (1916) 104-119. | JFM

[8] A. Schrijver, Bipartite edge coloring in 0(δm)time. SIAM J. Comput. 28 (1998) 841-846. | MR | Zbl

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