Abstract
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, log in via an institution to check access.
Similar content being viewed by others
References
G. Dirac: A property of 4-chromatic graphs and remarks on critical graphs,J. London Math. Soc.,27 (1952), 85–92.
R. J. Duffin: Topology of series-parallel networks,J. Math. Anal. Appl.,10 (1965), 303–318.
J. Edmonds: Maximum matching and a polyhedron with 0,1-vertices,J. Res. Nat. Bur. Standards Sect. B,69 (1965), 85–92.
M. Grötschel, L. Lovász, andA. Schrijver: The ellipsoid method and its consequences in combinatorial optimization,Combinatorica,1 (1981), 169–197.
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.
I. Holyer: The NP-completeness of edge-colouring,SIAM J. Comput.,10 (1981), 718–720.
O. Marcotte: On the chromatic index of multigraphs and a conjecture of Seymour (I),J. Combinatorial Theory, Ser. B,41 (1986), 306–331.
O.Marcotte: On the chromatic index of multigraphs and a conjecture of Seymour (II), preprint, (1987).
P. D. Seymour: Matroids and multicommodity flows,European J. Combinatorics,2 (1981), 257–290.
P. D. Seymour: On multicolourings of cubic graphs, and conjectures of Fulkerson and Tutte,Proc. London Math. Soc., (3)38 (1979), 423–460.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Seymour, P.D. Colouring series-parallel graphs. Combinatorica 10, 379–392 (1990). https://doi.org/10.1007/BF02128672
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02128672