# Interval Graphs: Canonical Representations in Logspace

## Abstract

### MSC codes

### Keywords

## Get full access to this article

View all available purchase options and get full access to this article.

## References

*Discrete Appl. Math.*, 88 (1998), pp. 7–28.

*J. Algorithms*, 21 (1996), pp. 542–564.

*Discrete Appl. Math.*, 155 (2007), pp. 442–456.

*J. Comput. System Sci.*, 13 (1976), pp. 335–379.

*Graph Classes: A Survey*, SIAM Monogr. Discrete Math. Appl. 3, SIAM, Philadelphia, 1999.

*Combinatorica*, 12 (1992), pp. 389–410.

*IEEE Trans. Parallel Distrib. Syst.*, 7 (1996), pp. 308–319.

*J. Comput. System Sci.*, 59 (1999), pp. 450–475.

*Inform. Process. Lett.*, 55 (1995), pp. 99–104.

*J. Algorithms*, 12 (1991), pp. 375–392.

*Networks*, 23 (1993), pp. 29–39.

*SIAM J. Comput.*, 25 (1996), pp. 390–403.

*Graph isomorphism for $K_{3,3}$-free and $K_5$-free graphs is in log-space*, in FSTTCS, Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2009, pp. 145–156.

*Planar graph isomorphism is in log-space*, in CCC, IEEE Computer Society, Washington, DC, 2009, pp. 203–214.

*Propriété de helly et problèmes de représentation*, in Problèmes Combinatoires et Théorie des Graphes (Orsay, 1976), Colloq. Int. CNRS 260, CNRS, Paris, France, 1978, pp. 117–118.

*Ann. Discrete Math.*, 21 (1984), pp. 67–96.

*J. Comput. System Sci.*, 54 (1997), pp. 400–411.

*Discrete Math.*, 225 (2000), pp. 149–172.

*Pacific J. Math.*, 15 (1965), pp. 835–855.

*Algorithmic Graph Theory and Perfect Graphs*, 2nd ed., Ann. Discrete Math. 57, Elsevier, New York, 2004.

*Testing graph isomorphism in parallel by playing a game*, in ICALP, Springer, Berlin, 2006, pp. 3–14.

*Theoret. Comput. Sci.*, 234 (2000), pp. 59–84.

*Discrete Math.*, 128 (1994), pp. 165–172.

*Theoret. Comput. Sci.*, 296 (2003), pp. 99–116

*SIAM J. Comput.*, 31 (2001), pp. 289–305.

*Group-Theoretic Algorithms and Graph Isomorphism*, Lecture Notes in Comput. Sci. 136, Springer, Berlin, 1982.

*SIAM J. Comput.*, 24 (1995), pp. 411–439.

*SIAM J. Comput.*, 28 (1999), pp. 1004–1020.

*SIAM J. Comput.*, 25 (1996), pp. 797–827.

*The isomorphism problem for k-trees is complete for logspace*, in MFCS, Springer, Berlin, 2009, pp. 537–548.

*J. Comput. System Sci.*, 37 (1988), pp. 190–246.

*The Graph Isomorphism Problem: Its Structural Complexity*, Progr. Theoret. Comput. Sci., Birkhäuser Boston, Boston, 1993.

*NC algorithms for comparability graphs, interval graphs, and testing for unique perfect matching*, in FSTTCS, Lecture Notes in Comput. Sci. 206, Springer, Berlin, 1985, pp. 496–503.

*Discrete Appl. Math.*, 52 (1994), pp. 233–252.

*Intersection graphs of noncrossing arc–connected sets in the plane*, in GD, Springer, Berlin, 1996, pp. 257–270.

*Capturing polynomial time on interval graphs*, in LICS, IEEE Computer Society, Washington, DC, 2010, pp. 199–208.

*A logspace algorithm for tree canonization*, in STOC, ACM, New York, 1992, pp. 400–404.

*J. ACM*, 26 (1979), pp. 183–195.

*Algorithmica*, 37 (2003), pp. 93–147.

*J. ACM*, 31 (1984), pp. 401–421.

*J. ACM*, 55 (2008), pp. 17.1–17.24.

*Indifference graphs*, in Proof Techniques in Graph Theory: Proceedings of the 2nd Annual Arbor Graph Theory Conference, Academic Press, New York, 1969, pp. 139–146.

*SIAM J. Comput.*, 5 (1976), pp. 266–283.

*Efficient Graph Representations*, Fields Inst. Monogr. 19, AMS, Providence, RI, 2003.

*J. Combin. Theory Ser. B*, 12 (1972), pp. 153–162.

*Simple geometrical intersection graphs*, in WALCOM, Lecture Notes in Comput. Sci. 4921, Springer, Berlin, 2008, pp. 25–33.

*IEEE Trans. Parallel Distrib. Syst.*, 7 (1996), pp. 3–10.

## Information & Authors

### Information

#### Published In

#### Copyright

#### History

**Submitted**: 29 July 2010

**Accepted**: 29 June 2011

**Published online**: 20 September 2011

#### MSC codes

#### Keywords

### Authors

## Metrics & Citations

### Metrics

### Citations

If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.

#### Cited By

- Compact representation of interval graphs and circular-arc graphs of bounded degree and chromatic numberTheoretical Computer Science, Vol. 941 | 1 Jan 2023
- Planar Graph Isomorphism is in Log-SpaceACM Transactions on Computation Theory, Vol. 204 | 26 July 2022
- Cyclic arrangements with minimum modulo m winding numbersGraphs and Combinatorics, Vol. 38, No. 3 | 14 March 2022
- Compact Representation of Interval Graphs of Bounded Degree and Chromatic Number2022 Data Compression Conference (DCC) | 1 Mar 2022
- The Weisfeiler–Leman Dimension of Chordal Bipartite Graphs Without Bipartite ClawGraphs and Combinatorics, Vol. 37, No. 3 | 25 March 2021
- Graph isomorphism restricted by listsTheoretical Computer Science, Vol. 860 | 1 Mar 2021
- Canonical Representations for Circular-Arc Graphs Using Flip SetsAlgorithmica, Vol. 80, No. 12 | 23 January 2018
- On the Parallel Parameterized Complexity of the Graph Isomorphism ProblemWALCOM: Algorithms and Computation | 31 January 2018
- On Compiling Structured CNFs to OBDDsTheory of Computing Systems, Vol. 61, No. 2 | 26 October 2016
- Circular-arc hypergraphs: Rigidity via connectednessDiscrete Applied Mathematics, Vol. 217 | 1 Jan 2017
- Solving the canonical representation and Star System Problems for proper circular-arc graphs in logspaceJournal of Discrete Algorithms, Vol. 38-41 | 1 May 2016
- On the isomorphism problem for Helly circular-arc graphsInformation and Computation, Vol. 247 | 1 Apr 2016
- Interval graph representation with given interval and intersection lengthsJournal of Discrete Algorithms, Vol. 34 | 1 Sep 2015
- On Compiling Structured CNFs to OBDDsComputer Science -- Theory and Applications | 23 June 2015
- Helly Circular-Arc Graph Isomorphism Is in LogspaceMathematical Foundations of Computer Science 2013 | 1 Jan 2013
- Interval Graph Representation with Given Interval and Intersection LengthsAlgorithms and Computation | 1 Jan 2012