Stretching a Knock-Knee Layout for Multilayer Wiring
IEEE Transactions on Computers
Discrete Mathematics
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Note: Edge intersection graphs of systems of paths on a grid with a bounded number of bends
Discrete Applied Mathematics
Journal of Computer and System Sciences
Recognizing d-interval graphs and d-track interval graphs
FAW'10 Proceedings of the 4th international conference on Frontiers in algorithmics
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
| Hi-index | 0.04 |
We investigate edge-intersection graphs of paths in the plane grid, regarding a parameter called the bend-number, i.e., every vertex is represented by a grid path and two vertices are adjacent if and only if the two grid paths share at least one grid-edge. The bend-number is the minimum k such that grid-paths with at most k bends each suffice to represent a given graph. This parameter is related to the interval-number and the track-number of a graph. We show that for every k there is a graph with bend-number k. Moreover we provide new upper and lower bounds of the bend-number of graphs in terms of degeneracy, treewidth, edge clique covers and the maximum degree. Furthermore we give bounds on the bend-number of K"m","n and determine it exactly for some pairs of m and n. Finally, we prove that recognizing single-bend graphs is NP-complete, providing the first such result in this field.