Skip to main content
SpringerLink
Log in

Colorings and orientations of graphs

  • Published:
Combinatorica Aims and scope Submit manuscript

Abstract

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).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. N. Alon, S. Friedland, andG. Kalai: Regular subgraphs of almost regular graphs,J. Combinatorial Theory, Ser. B37 (1984), 79–91.

    Article  MathSciNet  Google Scholar 

  2. N. Alon, C. McDiarmid, andB. Reed: Star Arboricity, to appear.

  3. N. Alon, andM. Tarsi: A nowhere zero point in linear mappings,Combinatorica 9 (1989), 393–395.

    Article  MathSciNet  Google Scholar 

  4. J. A. Bondy, R. Boppana, andA. Siegel: Private communication.

  5. C. Berge:Graphs and Hypergraphs, Dunod, Paris, 1970.

    MATH  Google Scholar 

  6. B. Bollobás:Extremal Graph Theory, Academic Press, New York, 1978.

    MATH  Google Scholar 

  7. A. Chetwynd, andR. Häggkvist: A note on list colorings,J. Graph Theory 13 (1989), 87–95.

    Article  MathSciNet  Google Scholar 

  8. P. Erdős: Some old and new problems in various branches of combinatorics,Congressus Numerantium 23 (1979), 19–37.

    MathSciNet  MATH  Google Scholar 

  9. P. Erdős, A. Rubin, andH. Taylor: Choosability in graphs,Congressus Numerantium 26 (1979), 125–157.

    MATH  Google Scholar 

  10. I. Gessel: Tournaments and Vandermonde's determinant,J. Graph Theory 3 (1979), 305–307.

    Article  MathSciNet  Google Scholar 

  11. 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.

    Article  Google Scholar 

  12. S.-Y. R. Li, andW.-C. W. Li: Independence numbers of graphs and generators of ideals,Combinatorical 1 (1981), 55–61.

    Article  MathSciNet  Google Scholar 

  13. R. P. Stanley: Acyclic orientations of graphs,Discrete Math. 5 (1973), 171–178.

    Article  MathSciNet  Google Scholar 

  14. M. Tarsi: On the decomposition of a graph into stars,Discrete Math. 36 (1981), 299–304.

    Article  MathSciNet  Google Scholar 

  15. 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.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Pure Mathematics School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel

    N. Alon

  2. Department of Computer Science School of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel

    M. Tarsi

Authors
  1. N. Alon
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Tarsi
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by a United States-Israel BSF Grant and by a Bergmann Memorial Grant.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Alon, N., Tarsi, M. Colorings and orientations of graphs. Combinatorica 12, 125–134 (1992). https://doi.org/10.1007/BF01204715

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01204715

AMS Subject Classification codes (1991)

Search

Navigation