Abstract
We show that the reachability problem for directed graphs that are either K 3,3-free or K 5-free is in unambiguous log-space, UL ∩ coUL. This significantly extends the result of Bourke, Tewari, and Vinodchandran that the reachability problem for directed planar graphs is in UL ∩ coUL.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Allender, E., Datta, S., Roy, S.: The directed planar reachability problem. In: Sarukkai, S., Sen, S. (eds.) FSTTCS 2005. LNCS, vol. 3821, pp. 238–249. Springer, Heidelberg (2005)
Asano, T.: An approach to the subgraph homeomorphism problem. Theoretical Computer Science 38 (1985)
Bourke, C., Tewari, R., Vinodchandran, N.: Directed planar reachability is in unambiguous log-space. In: Annual IEEE Conference on Computational Complexity (CCC), pp. 217–221 (2007)
Datta, S., Limaye, N., Nimbhorkar, P., Thierauf, T., Wagner, F.: Planar graph isomorphism is in log-space. Technical report, arXiv:0809.2319v2 (2009)
Hopcroft, J.E., Tarjan, R.E.: Dividing a graph into triconnected components. SIAM Journal on Computing 2(3), 135–158 (1973)
Khuller, S.: Parallel algorithms for K 5-minor free graphs. Technical Report TR88-909, Cornell University, Computer Science Department (1988)
Limaye, N., Mahajan, M., Nimbhorkar, P.: Longest paths in planar dags in unambiguous logspace. In: Computing: The Australian Theory Symposium (CATS), vol. 94 (2009)
Reingold, O.: Undirected st-connectivity in log-space. In: Proceedings of the 37th annual ACM Symposium on Theory of Computing (STOC), pp. 376–385 (2005)
Reinhardt, K., Allender, E.: Making nondeterminism unambiguous. SIAM Journal of Computing 29(4), 1118–1131 (2000)
Thierauf, T., Wagner, F.: The isomorphism problem for planar 3-connected graphs is in unambiguous logspace. In: Proceedings of the 25th Annual Symposium on Theoretical Aspects of Computer Science (STACS), pp. 633–644 (2008)
Tutte, W.T.: Connectivity in graphs. University of Toronto Press (1966)
Vazirani, V.V.: NC algorithms for computing the number of perfect matchings in K 3,3-free graphs and related problems. Information and Computation 80 (1989)
Wagner, K.: Über eine Eigenschaft der ebenen Komplexe. In: Mathematical Annalen, vol. 114 (1937)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Thierauf, T., Wagner, F. (2009). Reachability in K 3,3-Free Graphs and K 5-Free Graphs Is in Unambiguous Log-Space. In: Kutyłowski, M., Charatonik, W., Gębala, M. (eds) Fundamentals of Computation Theory. FCT 2009. Lecture Notes in Computer Science, vol 5699. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03409-1_29
Download citation
DOI: https://doi.org/10.1007/978-3-642-03409-1_29
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-03408-4
Online ISBN: 978-3-642-03409-1
eBook Packages: Computer ScienceComputer Science (R0)