Strong geodetic problem on complete multipartite graphs
Combinatorics
2018-06-04 v1
Abstract
The strong geodetic problem is to find the smallest number of vertices such that by fixing one shortest path between each pair, all vertices of the graph are covered. In this paper we study the strong geodetic problem on complete bipartite graphs; in particular, we discuss its asymptotic behavior. Some results for complete multipartite graphs are also derived. Finally, we prove that the strong geodetic problem restricted to (general) bipartite graphs is NP-complete.
Keywords
Cite
@article{arxiv.1806.00302,
title = {Strong geodetic problem on complete multipartite graphs},
author = {Vesna Iršič and Matjaž Konvalinka},
journal= {arXiv preprint arXiv:1806.00302},
year = {2018}
}
Comments
15 pages, 1 figure, 2 tables