Extending Partial Representations of Interval Graphs

[1]  Marcus Schaefer,et al.  Recognizing string graphs in NP , 2002, STOC '02.

[2]  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..

[3]  D. R. Fulkerson,et al.  Incidence matrices and interval graphs , 1965 .

[4]  Derek G. Corneil,et al.  A simple 3-sweep LBFS algorithm for the recognition of unit interval graphs , 2004, Discret. Appl. Math..

[5]  Anna Lubiw,et al.  The Simultaneous Representation Problem for Chordal, Comparability and Permutation Graphs , 2009, WADS.

[6]  Jan Kratochvíl,et al.  Testing planarity of partially embedded graphs , 2010, SODA '10.

[7]  Jan Kratochvíl,et al.  String graphs requiring exponential representations , 1991, J. Comb. Theory, Ser. B.

[8]  Stephan Olariu,et al.  Simple Linear Time Recognition of Unit Interval Graphs , 1995, Inf. Process. Lett..

[9]  C. Kuratowski Sur le problème des courbes gauches en Topologie , 1930 .

[10]  S. Benzer ON THE TOPOLOGY OF THE GENETIC FINE STRUCTURE. , 1959, Proceedings of the National Academy of Sciences of the United States of America.

[11]  Pavol Hell,et al.  Lexicographic orientation and representation algorithms for comparability graphs, proper circular arc graphs, and proper interval graphs , 1995, J. Graph Theory.

[12]  James F. Allen Maintaining knowledge about temporal intervals , 1983, CACM.

[13]  Xiaotie Deng,et al.  Linear-Time Representation Algorithms for Proper Circular-Arc Graphs and Proper Interval Graphs , 1996, SIAM J. Comput..

[14]  Anna Lubiw,et al.  Simultaneous Interval Graphs , 2010, ISAAC.

[15]  Ron Shamir,et al.  Complexity and algorithms for reasoning about time: a graph-theoretic approach , 1993, JACM.

[16]  Martin Charles Golumbic Reasoning About Time , 1992, AISMC.

[17]  Maurizio Patrignani On Extending a Partial Straight-line Drawing , 2006, Int. J. Found. Comput. Sci..

[18]  Jeremy P. Spinrad,et al.  Efficient graph representations , 2003, Fields Institute monographs.

[19]  Peter L. Hammer,et al.  Difference graphs , 1990, Discret. Appl. Math..

[20]  M. Golumbic Algorithmic graph theory and perfect graphs , 1980 .

[21]  F. Roberts Discrete Mathematical Models with Applications to Social, Biological, and Environmental Problems. , 1976 .

[22]  K. Stoffers Scheduling of traffic lights—A new approach☆ , 1968 .

[23]  Stephan Olariu,et al.  The LBFS Structure and Recognition of Interval Graphs , 2009, SIAM J. Discret. Math..

[24]  Pavel Klavík,et al.  Extending Partial Representations of Function Graphs and Permutation Graphs , 2012, ESA.

[25]  Jan Kratochvíl,et al.  String graphs. II. recognizing string graphs is NP-hard , 1991, J. Comb. Theory, Ser. B.

[26]  T. William,et al.  Surveys in Combinatorics, 1997: New Perspectives on Interval Orders and Interval Graphs , 1997 .

[27]  Robert E. Tarjan,et al.  Algorithmic Aspects of Vertex Elimination on Graphs , 1976, SIAM J. Comput..

[28]  Jiří Fiala NP completeness of the edge precoloring extension problem on bipartite graphs , 2003 .

[29]  Henry A. Kautz,et al.  Constraint Propagation Algorithms for Temporal Reasoning , 1986, AAAI.

[30]  Dániel Marx NP-completeness of list coloring and precoloring extension on the edges of planar graphs , 2005 .

[31]  Edward Szpilrajn-Marczewski Sur deux propriétés des classes d'ensembles , 1945 .