Abstract
Several intersection graphs such as curves-in-the-plane graphs, circular-arc graphs, chordal graphs and interval graphs are reviewed, especially on their recognition algorithms. In this connection graph realization problem is mentioned.
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F. Harary, Graph theory, Addison-Wesley, Reading Massachusetts (1972).
D.J. Rose, Triangulated graphs and the elimination process, J. Math. Anal. Appl., 32, 597–609 (1970).
T. Ohtsuki, H. Mori, E.S. Kuh, T. Kashiwabara and T. Fujisawa, One-dimensional gate assignment and interval graphs, IEEE tran. on CAS Vol. CAS-26, No.9, 675–684 (1979).
G. Ehrlich, S. Even and R.E. Tarjan, Intersection graphs of curves in the plane, J. Combinatorial theory (B), 21, 8–20 (1976).
S. Even and A. Itai, Queues, stacks and graphs, Theory of machines and computations, Z. Kohavi and A. Paz, ed., Academic Press, New York, 71–86 (1971).
M.R. Garey and D.S. Johnson, Computers and intractability: A guide to the theory of NP-completeness, H. Freeman and Sons, San Francisco (1978).
F. Gavril, Algorithms for a maximum clique and a maximum independent set of a circle graph, Network, 3, 261–273 (1973).
A. Tucker, An efficient test for circular-arc graphs, SIAM J. Comput., Vol.9, No.1, 1–24 (1980).
F. Gavril, The intersection graphs of subtrees in trees are exactly the chordal graphs, J. Combinatorial theory (B), 16, 47–56 (1974).
D.J. Rose, R.E. Tarjan and G.S. Lueker, Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput., Vol.5, No.2, 266–283 (1976).
F. Gavril, Algorithms for minimum coloring, maximum clique, minimum covering by cliques and maximum independent set of a chordal graph, SIAM J. Comput., 1, 180–187 (1972).
T. Oyamada and T. Ohtsuki, Interval graphs and layout design of MOS arrays, IECE technical report CST75–83 (1975) (in Japanese).
T. Yoshida, An algorithm for obtaining a perfect order of an interval graph, monograph, Osaka University (1976) (in Japanese).
K.S. Booth and G.S. Lueker, Testing for the consecutive ones property, interval graphs and graph planarity using PQ-tree algorithms J. Computer and System Sciences, 13, 335–379 (1976).
S. Fujishige, An efficient algorithm for solving the graph-realization problem by means of PQ-trees, Proceedings of 1979 ISCAS, IEEE catalog No. 79 CH 1421-7 CAS. 1012–1015 (1979).
S. Fujishige, An efficient algorithm for solving the graph-realization problem, IECE technical report CST78-136 (1979) (in Japanese).
A. Lempel, S. Even and I. Cederbaum, An algorithm for planarity testing of graphs, in "Theory of graphs: international Symposium: Rome, July, 1966" (P. Rosenstiehl, Ed.), 215–232, Gordon and Breach, New York (1967).
K.S. Booth, PQ-tree algorithms, Ph.D. Dissertation, Department of Electrical Engineering and Computer Sciences, University of California Berkeley, California (1975).
T. Kashiwabara and T. Fujisawa, An NP-complete problem on interval graph, Proceedings of 1979 ISCAS, 82–83 (1979).
T. Kashiwabara, Y. Masaki and T. Fujisawa, Complexity of inter-valization of graphs, IECE technical report CST77-15 (1977) (in Japanese).
G.S. Lueker, Efficient algorithms for chordal graphs and interval graphs, Ph.D. Dissertation, Program in Applied Mathematics and the Department of Electrical Engineering, Princeton University, Princeton N.J., (1975).
C.G. Lekkerkerker and J. Ch. Boland, Representation of a finite graph by a set of intervals on the real line, Fundamenta Mathematicae, 51, 45–64 (1962).
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Kashiwabara, T. (1981). Algorithms for some intersection graphs. In: Saito, N., Nishizeki, T. (eds) Graph Theory and Algorithms. Lecture Notes in Computer Science, vol 108. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-10704-5_15
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DOI: https://doi.org/10.1007/3-540-10704-5_15
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