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S. Masuda, K. Nakajima, T. Kashiwabara, T. Fujisawa, "Crossing Minimization in Linear Embeddings of Graphs," IEEE Transactions on Computers, vol. 39, no. 1, pp. 124127, January, 1990.  
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@article{ 10.1109/12.46286, author = {S. Masuda and K. Nakajima and T. Kashiwabara and T. Fujisawa}, title = {Crossing Minimization in Linear Embeddings of Graphs}, journal ={IEEE Transactions on Computers}, volume = {39}, number = {1}, issn = {00189340}, year = {1990}, pages = {124127}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.46286}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Crossing Minimization in Linear Embeddings of Graphs IS  1 SN  00189340 SP124 EP127 EPD  124127 A1  S. Masuda, A1  K. Nakajima, A1  T. Kashiwabara, A1  T. Fujisawa, PY  1990 KW  crossing minimisation; linear embeddings of graphs; circuit layout problems; NPhard; circuit layout CAD; computational complexity; graph theory; minimisation. VL  39 JA  IEEE Transactions on Computers ER   
The problem of embedding a graph in the plane with the minimum number of edge crossings arises in some circuit layout problems. It has been known to be NPhard in general. Recently, in the area of book embedding, this problem was shown to be NPhard even when the vertices are placed on a straight line l. The authors show that the problem remains NPhard even if, in addition to these constraints, the positions of the vertices on l are predetermined.
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