Stretching a Knock-Knee Layout for Multilayer Wiring
IEEE Transactions on Computers
Journal of Information Processing and Cybernetics
Eigenvalues, Expanders And Superconcentrators
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Edge-Intersection Graphs of k-Bend Paths in Grids
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
On the bend-number of planar and outerplanar graphs
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Approximation algorithms for B 1-EPG graphs
WADS'13 Proceedings of the 13th international conference on Algorithms and Data Structures
Edge-intersection graphs of grid paths: The bend-number
Discrete Applied Mathematics
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We answer some of the questions raised by Golumbic, Lipshteyn and Stern and obtain some other results about edge intersection graphs of paths on a grid (EPG graphs). We show that for any d=4, in order to represent every n vertex graph with maximum degree d as an edge intersection graph of n paths on a grid, a grid of area @Q(n^2) is needed. We also show several results related to the classes B"k-EPG, where B"k-EPG denotes the class of graphs that have an EPG representation such that each path has at most k bends. In particular, we prove: For a fixed k and a sufficiently large n, the complete bipartite graph K"m","n does not belong to B"2"m"-"3-EPG (it is known that this graph belongs to B"2"m"-"2-EPG); for any odd integer k we have B"k-EPG @?B"k"+"1-EPG; there is no number k such that all graphs belong to B"k-EPG; only 2^O^(^k^n^l^o^g^(^k^n^)^) out of all the 2^n^2 labeled graphs with n vertices are in B"k-EPG.