Bibliographic Details
| Title: |
Linkage on the infinite grid. |
| Authors: |
Jobson, Adam S.1 adam.jobson@louisville.edu, Kézdy, André E.1 andre.kezdy@louisville.edu, Lehel, Jenő1,2 j0lehe01@louisville.edu |
| Source: |
Information Processing Letters. Sep2018, Vol. 137, p51-56. 6p. |
| Subjects: |
Paired comparisons (Mathematics), Taxicab geometry, Geometric vertices, Angles, Euclidean distance, Euclidean domains |
| Abstract: |
For k fixed, a graph G is k-path-pairable , if for any set of k disjoint pairs of vertices, s i , t i , 1 ≤ i ≤ k , there exist pairwise edge-disjoint s i , t i -paths in G . Bounds on path-pairability are given here if G is the graph of the infinite integer grid in the Euclidean plane (vertices of G are the points of integer coordinates and two vertices are adjacent if and only if their Manhattan distance is 1). We prove that G is 10-path-pairable and at most 14-path-pairable. Related results and conjectures are summarized also for the integer halfplane, for the positive integer quadrant and for finite grids. [ABSTRACT FROM AUTHOR] |
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| Database: |
Engineering Source |
