Diameter computation on H-minor free graphs and graphs of bounded (distance) VC-dimension

Under the Strong Exponential-Time Hypothesis, the di-ameter of general unweighted graphs cannot be com-puted in truly subquadratic time. Nevertheless thereare several graph classes for which this can be donesuch as bounded-treewidth graphs, interval graphs andplanar graphs, to name a few. We propose to studyunweighted graphs of constant distance VC-dimensionas a broad generalization of many such classes – wherethe distance VC-dimension of a graph Gis defined asthe VC-dimension of its ball hypergraph: whose hyper-edges are the balls of all possible radii and centers in G.In particular for any fixed H, the class of H-minor freegraphs has distance VC-dimension at most |V(H)|−1.