English

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

R2 v1 2026-06-23T02:16:00.315Z