Antiflows, oriented and strong oriented colorings of graphs
Šámal, Robert
Archivum Mathematicum, Tome 040 (2004), p. 335-343 / Harvested from Czech Digital Mathematics Library
Access to full text
Full (PDF)

We present an overview of the theory of nowhere zero flows, in particular the duality of flows and colorings, and the extension to antiflows and strong oriented colorings. As the main result, we find the asymptotic relation between oriented and strong oriented chromatic number.

Publié le : 2004-01-01
Classification:  05C15 
@article{107917,
     author = {Robert \v S\'amal},
     title = {Antiflows, oriented and strong oriented colorings of graphs},
     journal = {Archivum Mathematicum},
     volume = {040},
     year = {2004},
     pages = {335-343},
     zbl = {1114.05032},
     mrnumber = {2129955},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107917}
}

Šámal, Robert. Antiflows, oriented and strong oriented colorings of graphs. Archivum Mathematicum, Tome 040 (2004) pp. 335-343. http://gdmltest.u-ga.fr/item/107917/

Devos M.; Nešetřil J.; Raspaud A. Antisymmetric Flows and Edge connectivity, Discrete Math. 276 (2004), No. 1-3, 161–167. | MR 2046631 | Zbl 1031.05062

Diestel R. Graph Theory, Springer 2000. | MR 1743598 | Zbl 1218.05001

Graham R. L.; Grotschel M.; Lovasz L. (Editors) Handbook of Combinatorics, North-Holland 1995. (1995)

Lang S. Algebra, Chapter I, §8, Springer 2002. | MR 1878556 | Zbl 1063.00002

Nešetřil J.; Raspaud A. Antisymmetric Flows and Strong Colourings of Oriented graphs, An. Inst. Fourier (Grenoble) 49, 3 (1999), 1037–1056. (1999) | MR 1703437 | Zbl 0921.05034

Rohrbach H.; Weis J. Zum finiten Fall des Bertrandschen Postulats, J. Reine Angew. Math., 214/5 (1964), 432–440. (1964) | MR 0161820 | Zbl 0131.04403

Singer J. A theorem in finite projective geometry and some applications to number theory, Trans. Amer. Math. Soc. 43 (1938) 377–385. (1938) | MR 1501951 | Zbl 0019.00502

Srinivasan B. R. On the number of Abelian groups of a given order, Acta Arith. 23 (1973), 195–205. (1973) | MR 0337841 | Zbl 0228.10022

Šámal R. Antisymmetric flows and strong oriented coloring of planar graphs, EuroComb’01 (Barcelona), Discrete Math. 273 (2003), no. 1-3, 203–209. | MR 2025951 | Zbl 1029.05054

Šámal R. Flows and Colorings of Graphs, Proceedings of the conference Week of Doctoral Students 2002, Charles University in Prague, Faculty of Mathematics and Physics.