research-article

A Linear Recognition Algorithm for Cographs

Authors:

D. G. Corneil,

Y. Perl,

L. K. StewartAuthors Info & Claims

SIAM Journal on Computing, Volume 14, Issue 4

Pages 926 - 934

https://doi.org/10.1137/0214065

Published: 01 November 1985 Publication History

Abstract

Cographs are the graphs formed from a single vertex under the closure of the operations of union and complement. Another characterization of cographs is that they are the undirected graphs with no induced paths on four vertices. Cographs arise naturally in such application areas as examination scheduling and automatic clustering of index terms. Furthermore, it is known that cographs have a unique tree representation called a cotree. Using the cotree it is possible to design very fast polynomial time algorithms for problems which are intractable for graphs in general. Such problems include chromatic number, clique determination, clustering, minimum weight domination, isomorphism, minimum fill-in and Hamiltonicity. In this paper we present a linear time algorithm for recognizing cographs and constructing their cotree representation.

References

[1]

Kellogg S. Booth, George S. Lueker, Testing for the consecutive ones property, interval graphs, and graph planarity using $PQ$-tree algorithms, J. Comput. System Sci., 13 (1976), 335–379

Digital Library

Google Scholar

[2]

S. A. Cook, The complexity of theorem-proving procedures, Proc. 3rd Annual ACM Symposium on Theory of Computing, ACM, New York, 1971, 151–158

Google Scholar

[3]

D. G. Corneil, H. Lerchs, L. Stewart Burlingham, Complement reducible graphs, Discrete Appl. Math., 3 (1981), 163–174

Crossref

Google Scholar

[4]

D. G. Corneil, Y. Perl, Clustering and domination in perfect graphs, Discrete Appl. Math., 9 (1984), 27–39

Crossref

Google Scholar

[5]

D. G. Corneil, Y. Perl, L. Stewart, Cographs: recognition, applications and algorithms, Congr. Numer., 43 (1984), 249–258

Google Scholar

[6]

Michael R. Garey, David S. Johnson, Computers and intractability, W. H. Freeman and Co., San Francisco, Calif., 1979x+338, A Guide to the Theory of NP-completeness

Digital Library

Google Scholar

[7]

C. C. Gotlieb, S. Kumar, Semantic clustering of index terms, J. Assoc. Comput. Mach., 15 (1968), 493–513

Digital Library

Google Scholar

[8]

J. E. Hopcroft, R. E. Tarjan, Efficient planarity testing, J. Assoc. Comput. Mach., 21 (1974), 549–568

Digital Library

Google Scholar

[9]

R. M. Karp, On the complexity of combinatorial problems, Networks, 5 (1975), 45–68

Digital Library

Google Scholar

[10]

Donald J. Rose, R. Endre Tarjan, George S. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput., 5 (1976), 266–283

Digital Library

Google Scholar

[11]

J. Spinrad, Transitive orientation in O(n2) time, Proc. 15th Annual ACM Symposium on Theory of Computing, ACM, New York, 1983, 457–466

Google Scholar

[12]

L. Stewart, Cographs, a class of tree representable graphs, TR 126/78, Dept. Computer Science, Univ. Toronto, Toronto, Ontario, 1978

Google Scholar

[13]

Jacobo Valdes, Robert E. Tarjan, Eugene L. Lawler, The recognition of series parallel digraphs, SIAM J. Comput., 11 (1982), 298–313

Digital Library

Google Scholar

Cited By

View all

Brosse CLagoutte ALimouzy VMary APastor L(2024)Efficient enumeration of maximal split subgraphs and induced sub-cographs and related classesDiscrete Applied Mathematics10.1016/j.dam.2023.10.025345:C(34-51)Online publication date: 15-Mar-2024
https://dl.acm.org/doi/10.1016/j.dam.2023.10.025
Chaudhary JPradhan D(2024)Roman {3}-domination in graphsDiscrete Applied Mathematics10.1016/j.dam.2022.09.017354:C(301-325)Online publication date: 15-Sep-2024
https://dl.acm.org/doi/10.1016/j.dam.2022.09.017
Papadopoulos CZisis A(2024)Computing and Listing Avoidable Vertices and PathsAlgorithmica10.1007/s00453-023-01168-286:1(281-306)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s00453-023-01168-2
Show More Cited By

Index Terms

A Linear Recognition Algorithm for Cographs
1. Mathematics of computing
  1. Discrete mathematics
    1. Combinatorics
    2. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Design and analysis of algorithms
  2. Randomness, geometry and discrete structures

Index terms have been assigned to the content through auto-classification.

Recommendations

Cycle transversals in perfect graphs and cographs

A cycle transversal (or feedback vertex set) of a graph G is a subset T@__ __V(G) such that T@__ __V(C)<>0@__ __ for every cycle C of G. This work considers the problem of finding special cycle transversals in perfect graphs and cographs. We prove that ...
Polar cographs

Polar graphs are a natural extension of some classes of graphs like bipartite graphs, split graphs and complements of bipartite graphs. A graph is (s,k)-polar if there exists a partition A,B of its vertex set such that A induces a complete s-partite ...
Linear-time algorithm for the matched-domination problem in cographs

Let G=(V, E) be a graph without isolated vertices. A matching in G is a set of independent edges in G. A perfect matching M in G is a matching such that every vertex of G is incident to an edge of M. A set S⊆ V is a paired-dominating set of G if every ...

Comments

Information & Contributors

Information

Published In

SIAM Journal on Computing Volume 14, Issue 4

Nov 1985

292 pages

ISSN:0097-5397

DOI:10.1137/smjcat.1985.14.issue-4

Issue’s Table of Contents

Publisher

Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 November 1985

Author Tags

Qualifiers

Research-article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

28
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 15 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Brosse CLagoutte ALimouzy VMary APastor L(2024)Efficient enumeration of maximal split subgraphs and induced sub-cographs and related classesDiscrete Applied Mathematics10.1016/j.dam.2023.10.025345:C(34-51)Online publication date: 15-Mar-2024
https://dl.acm.org/doi/10.1016/j.dam.2023.10.025
Chaudhary JPradhan D(2024)Roman {3}-domination in graphsDiscrete Applied Mathematics10.1016/j.dam.2022.09.017354:C(301-325)Online publication date: 15-Sep-2024
https://dl.acm.org/doi/10.1016/j.dam.2022.09.017
Papadopoulos CZisis A(2024)Computing and Listing Avoidable Vertices and PathsAlgorithmica10.1007/s00453-023-01168-286:1(281-306)Online publication date: 1-Jan-2024
https://dl.acm.org/doi/10.1007/s00453-023-01168-2
Contreras-Mendoza FHernández-Cruz C(2024)Minimal Obstructions for Polarity, Monopolarity, Unipolarity and (s, 1)-Polarity in Generalizations of CographsGraphs and Combinatorics10.1007/s00373-024-02784-740:3Online publication date: 9-Apr-2024
https://dl.acm.org/doi/10.1007/s00373-024-02784-7
Le HLe V(2024)Complexity of the (Connected) Cluster Vertex Deletion Problem on H-free GraphsTheory of Computing Systems10.1007/s00224-024-10161-368:2(250-270)Online publication date: 1-Apr-2024
https://dl.acm.org/doi/10.1007/s00224-024-10161-3
Gurski FRothe JWeishaupt R(2024)Stability, Vertex Stability, and Unfrozenness for Special Graph ClassesTheory of Computing Systems10.1007/s00224-023-10149-568:1(75-102)Online publication date: 1-Feb-2024
https://dl.acm.org/doi/10.1007/s00224-023-10149-5
Mondal JVijayakumar S(2024)Star Covers and Star Partitions of Cographs and Butterfly-free GraphsAlgorithms and Discrete Applied Mathematics10.1007/978-3-031-52213-0_16(224-238)Online publication date: 15-Feb-2024
https://dl.acm.org/doi/10.1007/978-3-031-52213-0_16
Oostveen Jvan Leeuwen E(2023)Streaming deletion problems parameterized by vertex coverTheoretical Computer Science10.1016/j.tcs.2023.114178979:COnline publication date: 10-Nov-2023
https://dl.acm.org/doi/10.1016/j.tcs.2023.114178
Gutierrez MProtti FTondato S(2023)Convex geometries over induced paths with bounded lengthDiscrete Mathematics10.1016/j.disc.2022.113133346:1Online publication date: 1-Jan-2023
https://dl.acm.org/doi/10.1016/j.disc.2022.113133
Wahid DHassini E(2023)User-generated short-text classification using cograph editing-based network clustering with an application in invoice categorizationData & Knowledge Engineering10.1016/j.datak.2023.102238148:COnline publication date: 1-Nov-2023
https://dl.acm.org/doi/10.1016/j.datak.2023.102238
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Index Terms

Recommendations

Cycle transversals in perfect graphs and cographs

Polar cographs

Linear-time algorithm for the matched-domination problem in cographs

Comments

Information

Published In

Publisher

Publication History

Author Tags

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations