Colorings and orientations of graphs
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Bounds for the chromatic number and for some related parameters of a graph are obtained by applying algebraic techniques. In particular, the following result is proved: IfG is a directed graph with maximum outdegreed, and if the number of Eulerian subgraphs ofG with an even number of edges differs from the number of Eulerian subgraphs with an odd number of edges then for any assignment of a setS(v) ofd+1 colors for each vertexv ofG there is a legal vertex-coloring ofG assigning to each vertexv a color fromS(v).
- N. Alon, S. Friedland, andG. Kalai: Regular subgraphs of almost regular graphs,J. Combinatorial Theory, Ser. B37 (1984), 79–91.
- N. Alon, C. McDiarmid, andB. Reed: Star Arboricity, to appear.
- N. Alon, andM. Tarsi: A nowhere zero point in linear mappings,Combinatorica 9 (1989), 393–395.
- J. A. Bondy, R. Boppana, andA. Siegel: Private communication.
- C. Berge:Graphs and Hypergraphs, Dunod, Paris, 1970.
- B. Bollobás:Extremal Graph Theory, Academic Press, New York, 1978.
- A. Chetwynd, andR. Häggkvist: A note on list colorings,J. Graph Theory 13 (1989), 87–95.
- P. Erdős: Some old and new problems in various branches of combinatorics,Congressus Numerantium 23 (1979), 19–37.
- P. Erdős, A. Rubin, andH. Taylor: Choosability in graphs,Congressus Numerantium 26 (1979), 125–157.
- I. Gessel: Tournaments and Vandermonde's determinant,J. Graph Theory 3 (1979), 305–307.
- R. L. Graham, S.-Y. R. Li, andW.-C. W. Li: On the structure oft-designs,SIAM J. Alg. Disc. Meth. 1 (1980), 8–14.
- S.-Y. R. Li, andW.-C. W. Li: Independence numbers of graphs and generators of ideals,Combinatorical 1 (1981), 55–61.
- R. P. Stanley: Acyclic orientations of graphs,Discrete Math. 5 (1973), 171–178.
- M. Tarsi: On the decomposition of a graph into stars,Discrete Math. 36 (1981), 299–304.
- V. G. Vizing: Coloring the vertices of a graph in prescribed colors (in Russian),Diskret. Analiz. 29,Metody Discret. Anal. v. Teorii Kodov i Shem 101 (1976), 3–10.
- Colorings and orientations of graphs
Volume 12, Issue 2 , pp 125-134
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- 1. Department of Pure Mathematics School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel
- 2. Department of Computer Science School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel