Strong geodetic problem on complete multipartite graphs
Vesna Ir\v{s}i\v{c}, Matja\v{z} Konvalinka
TL;DR
This paper investigates the strong geodetic problem on complete bipartite and multipartite graphs, analyzing its asymptotic behavior and proving NP-completeness for bipartite graphs.
Contribution
It provides new results on the strong geodetic problem for complete multipartite graphs and establishes NP-completeness for bipartite graphs.
Findings
Asymptotic behavior characterized for complete bipartite graphs
Results extended to complete multipartite graphs
NP-completeness proven for bipartite graphs
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.