کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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418776 | 681718 | 2014 | 19 صفحه PDF | دانلود رایگان |
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 kk such that grid-paths with at most kk 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 kk there is a graph with bend-number kk. 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 Km,nKm,n and determine it exactly for some pairs of mm and nn. Finally, we prove that recognizing single-bend graphs is NP-complete, providing the first such result in this field.
Journal: Discrete Applied Mathematics - Volume 167, 20 April 2014, Pages 144–162