Colouring series-parallel graphs


We establish a minimax formula for the chromatic index of series-parallel graphs; and also prove the correctness of a “greedy” algorithm for finding a vertex-colouring of a series-parallel graph.

This is a preview of subscription content, access via your institution.


  1. [1]

    G. Dirac: A property of 4-chromatic graphs and remarks on critical graphs,J. London Math. Soc.,27 (1952), 85–92.

    Google Scholar 

  2. [2]

    R. J. Duffin: Topology of series-parallel networks,J. Math. Anal. Appl.,10 (1965), 303–318.

    Article  Google Scholar 

  3. [3]

    J. Edmonds: Maximum matching and a polyhedron with 0,1-vertices,J. Res. Nat. Bur. Standards Sect. B,69 (1965), 85–92.

    Google Scholar 

  4. [4]

    M. Grötschel, L. Lovász, andA. Schrijver: The ellipsoid method and its consequences in combinatorial optimization,Combinatorica,1 (1981), 169–197.

    Google Scholar 

  5. [5]

    A. J. Hoffman: Some recent applications of the theory of linear inequalities to extremal combinatorial analysis,Combinatorial Analysis, Proc. Symp. Appl. Math.,10 (1960), 113–127.

    Google Scholar 

  6. [6]

    I. Holyer: The NP-completeness of edge-colouring,SIAM J. Comput.,10 (1981), 718–720.

    Google Scholar 

  7. [7]

    O. Marcotte: On the chromatic index of multigraphs and a conjecture of Seymour (I),J. Combinatorial Theory, Ser. B,41 (1986), 306–331.

    Google Scholar 

  8. [8]

    O.Marcotte: On the chromatic index of multigraphs and a conjecture of Seymour (II), preprint, (1987).

  9. [9]

    P. D. Seymour: Matroids and multicommodity flows,European J. Combinatorics,2 (1981), 257–290.

    Google Scholar 

  10. [10]

    P. D. Seymour: On multicolourings of cubic graphs, and conjectures of Fulkerson and Tutte,Proc. London Math. Soc., (3)38 (1979), 423–460.

    Google Scholar 

Download references

Author information



Rights and permissions

Reprints and Permissions

About this article

Cite this article

Seymour, P.D. Colouring series-parallel graphs. Combinatorica 10, 379–392 (1990).

Download citation

AMS subject classification (1980)

  • 05 C 15