1 research outputs found
Geodesic packing in graphs
Given a graph , a geodesic packing in is a set of vertex-disjoint
maximal geodesics, and the geodesic packing number of , {\gpack}(G), is
the maximum cardinality of a geodesic packing in . It is proved that the
decision version of the geodesic packing number is NP-complete. We also
consider the geodesic transversal number, , which is the minimum
cardinality of a set of vertices that hit all maximal geodesics in . While
\gt(G)\ge \gpack(G) in every graph , the quotient is investigated. By using the rook's graph, it is proved that there
does not exist a constant such that would hold for all graphs . If is a tree, then it is
proved that , and a linear algorithm for
determining is derived. The geodesic packing number is also
determined for the strong product of paths