Bipartite permutation graphs

This paper examines the class of bipartite permutation graphs. Two characterizations of graphs in this class are presented. These characterizations lead to a linear time recognition algorithm, and to polynomial time algorithms for a number of NP-complete problems when restricted to graphs in this class.

[1]  Charles J. Colbourn,et al.  On testing isomorphism of permutation graphs , 1981, Networks.

[2]  P. Gilmore,et al.  A Characterization of Comparability Graphs and of Interval Graphs , 1964, Canadian Journal of Mathematics.

[3]  M. Yannakakis.  Computing the Minimum Fill-in is NP^Complete , 1981 .

[4]  Amir Pnueli,et al.  Permutation Graphs and Transitive Graphs , 1972, JACM.

[5]  Jeremy P. Spinrad,et al.  On Comparability and Permutation Graphs , 1985, SIAM J. Comput..

[6]  A. Lempel,et al.  Transitive Orientation of Graphs and Identification of Permutation Graphs , 1971, Canadian Journal of Mathematics.

[7]  T. Gallai.  Transitiv orientierbare Graphen , 1967 .

[8]  G. Tinhofer.  Graphen und Matrizen , 1976 .

[9]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[10]  Dieter Kratsch,et al.  On Domination Problems for Permutation and Other Graphs , 1987, Theor. Comput. Sci..

[11]  J. Keil,et al.  Finding minimum dominating cycles in permutation graphs , 1985 .

[12]  D. Rose.  Triangulated graphs and the elimination process , 1970 .

[13]  George Steiner,et al.  A linear time algorithm to find the jump number of 2-dimensional bipartite partial orders , 1987 .

[14]  Nobuji Saito,et al.  NP-Completeness of the Hamiltonian Cycle Problem for Bipartite Graphs , 1980 .

[15]  Kellogg S. Booth,et al.  Testing for the Consecutive Ones Property, Interval Graphs, and Graph Planarity Using PQ-Tree Algorithms , 1976, J. Comput. Syst. Sci..

[16]  Lorna Stewart.  Permutation graph structure and algorithms , 1985 .

[17]  M. S. Krishnamoorthy,et al.  An NP-hard problem in bipartite graphs , 1975, SIGA.

[18]  Richard M. Karp,et al.  A n^5/2 Algorithm for Maximum Matchings in Bipartite Graphs , 1971, SWAT.

[19]  R. Möhring.  Algorithmic graph theory and perfect graphs , 1986 .

[20]  David S. Johnson,et al.  The NP-Completeness Column: An Ongoing Guide , 1982, J. Algorithms.

[21]  J. A. Bondy,et al.  Graph Theory with Applications , 1978 .

[22]  Martin Farber,et al.  Domination in Permutation Graphs , 1985, J. Algorithms.

[23]  S. F. Kapoor,et al.  The Many Facets of Graph Theory , 1969 .

[24]  Dieter Kratsch,et al.  On the restriction of some NP-complete graph problems to permutation graphs , 1985, FCT.

[25]  J. Spinrad.  Two-dimensional partial orders , 1982 .

[26]  Jayme Luiz Szwarcfiter,et al.  Hamilton Paths in Grid Graphs , 1982, SIAM J. Comput..