Minimum diameter and cycle-diameter orientations on planar graphs
Discrete Mathematics
2011-05-25 v1 Computational Complexity
Abstract
Let G be an edge weighted undirected graph. For every pair of nodes consider the shortest cycle containing these nodes in G. The cycle diameter of G is the maximum length of a cycle in this set. Let H be a directed graph obtained by directing the edges of G. The cycle diameter of H is similarly defined except for that cycles are replaced by directed closed walks. Is there always an orientation H of G whose cycle diameter is bounded by a constant times the cycle diameter of G? We prove this property for planar graphs. These results have implications on the problem of approximating an orientation with minimum diameter
Keywords
Cite
@article{arxiv.1105.4770,
title = {Minimum diameter and cycle-diameter orientations on planar graphs},
author = {Nili Guttmann-Beck and Refael Hassin},
journal= {arXiv preprint arXiv:1105.4770},
year = {2011}
}