Parameterized Complexity of Geodetic Set
A vertex set S of a graph G is geodetic if every vertex of G lies on a shortest path between two vertices in S. Given a graph G and k N, the NP-hard GEODETIC S ET problem asks whether there is a geodetic set of size at most k. Complementing various works on GEODETIC S ET restricted to special graph classes, we initiate a parameterized complexity study of GEODETIC S ET and show, on the one side, that GEODETIC S ET is W[1]-hard when parameterized by feedback vertex number, path-width, and solution size, combined. On the other side, we develop fixed-parameter algorithms with respect to the feedback edge number, the tree-depth, and the modular-width of the input graph., number=4, journal=Journal of Graph Algorithms and Applications, author=Kellerhals, Leon and Koana, Tomohiro, year=2022, month=Jul., pages=401–419