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            <title xml:lang="en">Diameter, eccentricities and distance oracle computations on H-minor free graphs and graphs of bounded (distance) VC-dimension</title>
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                <forename type="first">Guillaume</forename>
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            <funder>This work was supported by Inria Gang project-team, by Irif laboratory from CNRS and Paris  University, and by the ANR projects DISTANCIA (ANR-17-CE40-0015) and Multimod (ANR-17-CE22-0016). This work was also supported by project PN 19 37 04 01 “New solutions for complex problems in current ICT research ﬁelds based on modelling and optimization”, funded  by the Romanian Core Program of the Ministry of Research and Innovation (MCI) 2019-2022,  and by a grant of Romanian Ministry of Research and Innovation CCCDI-UEFISCDI, project no. 17PCCDI/2018.</funder>
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              <p>Under the Strong Exponential-Time Hypothesis, the diameter of general unweighted graphs cannot be computed in truly subquadratic time (in the size n + m of the input), as shown by Roditty and Williams. Nevertheless there are several graph classes for which this can be done such as bounded-treewidth graphs, interval graphs and planar graphs, to name a few. We propose to study unweighted graphs of constant distance VC-dimension as a broad generalization of many such classes-where the distance VC-dimension of a graph G is defined as the VCdimension of its ball hypergraph: whose hyperedges are the balls of all possible radii and centers in G. In particular for any fixed H, the class of H-minor free graphs has distance VC-dimension at most |V (H)| − 1.</p>
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