Abstract
We show that every Halin and every outerplanar graph can be optimally edge-coloured in polylog time using a polynomial number of processors on a parallel random access machine without write conflicts (P-RAM). Our algorithms are designed using the divide and conquer technique in a parallel setting.
On leave from the Department of Informatics, Warsaw University.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
K.Diks. A fast parallel algorithm for six-colouring of planar graphs. Math. Found.of Computer Science,Bratislava,1986, Lect.Notes in Comp.Science
S. Fiorini and R.J. Wilson. Edge-colouring of graphs, Research Notes in Mathematics 16, Pitman, London 1977.
S. Fiorini. On the chromatic index of outerplanar graphs, J.Comb. Theory (B) 18 (1975), 35–38.
S.Fortune and J.Wyllie. Parallelism in random access machines, 10th ACM Symp.Theory of Computing (1978),114–118.
H. Gabow and O. Kariv. Algorithms for edge colouring bipartite graphs and multigraphs, SIAM J.Computing 11,1 (1982),117–129.
A. M. Gibbons and W. Rytter. A fast parallel algorithm for optimally edge-colouring outerplanar graphs. Report No.80. Dept.of Computer Science, University of Warwick.(1986).
I. Holyer. The NP-completeness of edge-colouring. SIAM J.Comp. 10 (1981) 718–720
J. Ja'Ja and J. Simon. Parallel algorithms in graph theory: planarity testing. SIAM J. Comp. 10 (1981) 718–720.
G.F. Lev, N. Pippenger and L.G. Valiant. A fast parallel algorithm for routing in permutation networks. IEEE Trans. on Computers, C-30,2 (1981),93–100.
A.Proskurowski and M.Syslo. Efficient vertex-and edge-colouring of outerplanar graphs. SIAM J.Algebraic and Discrete methods (1986).
M.Skowronska. Efficient vertex and edge colouring of Halin graphs. Proc.3rd Czechoslovak Symp. on Graph Theory, Praque 1982.
M.Syslo. NP-complete problems on some tree structured graphs: a review, WG'83 Intern. Workshop on Graph Theoretic Concepts in Comp.Science, (M.Nagl, J.Perl, editors) 342–353 (1983)
M.Syslo, A Proskurowski. On Halin graphs. Proc. Graph Theory, Lect. Notes on Math., Springer-Verlag (1983)
R.E. Tarjan, U. Vishkin. Finding biconnected components and computing tree functions in logarithmic parallel time. FOCS (1984) 12–20, also SIAM J.Computing 14:4 (1985),862–874
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gibbons, A., Rytter, W. (1987). Fast parallel algorithms for optimal edge-colouring of some tree-structured graphs. In: Budach, L., Bukharajev, R.G., Lupanov, O.B. (eds) Fundamentals of Computation Theory. FCT 1987. Lecture Notes in Computer Science, vol 278. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18740-5_36
Download citation
DOI: https://doi.org/10.1007/3-540-18740-5_36
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-18740-0
Online ISBN: 978-3-540-48138-6
eBook Packages: Springer Book Archive