Dynamic Programming Algorithms on Directed Cographs

  • Frank Gurski University of Duesseldorf
Keywords: directed cograph, digraph, dynamic programming


In this paper we consider directed cographs, which are defined by Bechet et al. by the disjoint union, series, and order composition, from an algorithmic point of view. Using their recursive structure we give dynamic programming algorithms to show that for every directed cograph the size of a largest edgeless subdigraph, the size of a largest subdigraph which is a tournament, the size of a largest semicomplete subdigraph, and the size of a largest complete subdigraph can be computed in linear time. Our main results show that the hamiltonian path, hamiltonian cycle, regular subdigraph, and directed cut problem are polynomial on directed cographs.


J. Bang-Jensen and G. Gutin. Digraphs. Theory, Algorithms and Applications. Springer-Verlag, Berlin, 2009.

J. Bang-Jensen and A. Maddaloni. Arc-disjoint paths in decomposable digraphs. Journal of Graph Theory, 77:89--110, 2014.

D. Bechet, P. de Groote, and C. Retore. A complete axiomatisation of the inclusion of series-parallel partial orders. In Rewriting Techniques and Applications, volume 1232 of LNCS, pages 230--240. Springer-Verlag, 1997.

H.L. Bodlaender. Achromatic number is NP-complete for cographs and interval graphs. Information Processing Letters, 31(3):135--138, 1989.

M. Burlet and J.P. Uhry. Parity graphs. Annals of Discrete Mathematics, 21:253--277, 1984.

D.G. Corneil, H. Lerchs, and L. Stewart-Burlingham. Complement reducible graphs. Discrete Applied Mathematics, 3:163--174, 1981.

C. Crespelle and C. Paul. Fully dynamic recognition algorithm and certificate for directed cographs. Discrete Applied Mathematics, 154(12):1722--1741, 2006.

D.G. Corneil, Y. Perl, and L.K. Stewart. A linear recognition algorithm for cographs. SIAM Journal on Computing, 14(4):926--934, 1985.

S. Friedlan. Every 7-regular digraph contains an even cycle. Journal of Combinatorial Theory, Series B, 46(2):249--252, 1989.

F. Gurski and E. Wanke. Vertex disjoint paths on clique-width bounded graphs. Theoretical Computer Science, 359(1-3):188--199, 2006.

M. Habib and C. Paul. A simple linear time algorithm for cograph recognition. Discrete Applied Mathematics, 145:183--197, 2005.

H.A. Jung. On a class of posets and the corresponding comparability graphs. Journal of Combinatorial Theory, Series B, 24:125--133, 1978.

H. Lerchs. On cliques and kernels. Technical report, Dept. of Comput. Sci, Univ. of Toronto, 1971.

C. Retore. Pomset logic as a calculus of directed cographs. In Fourth Roma Workshop: Dynamic perspectives in Logic and Linguistics, pages 221--247. CLUEB, 1999.

E. Sopena. Oriented graph coloring. Discrete Mathematics, 229:359--369, 2001.

P.D. Sumner. Dacey graphs. Journal of Aust. Soc., 18:492--502, 1974.

How to Cite
Gurski, F. (2017). Dynamic Programming Algorithms on Directed Cographs. Statistics, Optimization & Information Computing, 5(1), 35-44. https://doi.org/10.19139/soic.v5i1.260
Research Articles