Abstract
For a graph G=(V, E) its line graph L(G) has the node set E and two nodes of L(G) are adjacent if the corresponding edges of G have a common endpoint. The problem of finding G for a given L was already optimally solved by Lehot[7] and Roussopoulos[11]. Here we present a new dynamic solution to this problem, where we can add or delete a node v in L(G) in time proportional to the size of its adjacency list.
This author was partially supported by the Swiss National Science Foundation
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
D. Eppstein, Z. Galil, G.F. Italiano and T. Spencer. Separator based sparsification for dynamic planar graph algorithms. Proc. 25th Annual Symp. on Theory of Computing (1993), 208–217.
M. R. Garey and D. S. Johnson. Computers and Intractability. A Guide to the Theory of NP-Completeness. W. Freeman and Company, 1979.
M. C. Golumbic. Algorithmic Graph Theory and Perfect Graphs, Academic Press, 1980.
F. Harary. Graph Theory, Addison-Wesley, 1969.
H. A. Jung. Zu einem Isomorphiesatz von H. Whitney für Graphen. Math. Annalen164 (1966), 270–271.
J. Krausz. Démonstration nouvelle d'un théorème de Whitney sur les résaux. Mat. Fiz. Lapok50(1943), 75–85.
P. G. H. Lehot. An Optimal Algorithm to Detect a Line Graph and Output Its Root Graph. Journal of the ACM21(1974), 569–575.
J. Naor and M.B. Novick. An Efficient Reconstruction of a Graph from Its Line Graph in Parallel. Journal of Algorithms11(1990), 132–143.
O. Ore. Theory of Graphs, American Mathematical Society Colloquium Publications, 38(1962).
M. Rauch. Improved data structures for fully dynamic biconnectivity. Proc. 26th Annual Symp. on Theory of Computing (1994), 686–695.
N. D. Roussopoulos. A max{m, n} Algorithm for Detecting the Graph H from its Line Graph G. Information Processing Letters2(1973), 108–112.
K. Simon. Effiziente Algorithmen für perfekte Graphen. B. G. Teubner, Stuttgart, 1992.
H.-P. Schmocker. Erkennung von Kantengraphen. Diploma thesis, Institut für Theoretische Informatik, ETH Zürich, 1991.
A. C. M. van Rooij and H. S. Wilf. The Interchange Graph of a Finite Graph. Acta Mathematica Academiae Scientiarum Hungaricae16(1965), 263–269.
H. Whitney. Congruent Graphs and the Connectivity of Graphs. American Journal of Mathematics54(1932), 150–168.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Degiorgi, D.G., Simon, K. (1995). A dynamic algorithm for line graph recognition. In: Nagl, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 1995. Lecture Notes in Computer Science, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60618-1_64
Download citation
DOI: https://doi.org/10.1007/3-540-60618-1_64
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60618-5
Online ISBN: 978-3-540-48487-5
eBook Packages: Springer Book Archive