Hitting Geodesic Intervals is NP-complete on graphs that are almost disjoint paths or triangles, yet becomes fixed-parameter tractable when the solution size is combined with modular-width, vertex integrity, or multiway-cut parameters.
Agarwal, Sariel Har - Peled, Rahul Raychaudhury, and Stavros Sintos
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Hitting Geodesic Intervals in Structurally Restricted Graphs
Hitting Geodesic Intervals is NP-complete on graphs that are almost disjoint paths or triangles, yet becomes fixed-parameter tractable when the solution size is combined with modular-width, vertex integrity, or multiway-cut parameters.