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                * Princeton Discrete Math Seminar *
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Speaker: Himanshu Gupta, University of Delaware

Thursday 29th September, 3:00 in Fine Hall 224.

Title: The least Euclidean distortion constant of a distance-regular graph


Embedding graphs into Euclidean spaces with least distortion is a topic well-studied in 
mathematics and computer science. Despite this research, there are just a few graphs for 
which the precise least distortion and a least distortion embedding is known. In 2008, 
Vallentin studied this problem for distance-regular graphs and obtained a lower bound for 
the least distortion of a distance-regular graph. In addition, he showed that this bound 
is tight for Hamming and Johnson graphs as well as strongly regular graphs and conjectured 
that his bound is always tight for distance-regular graphs. In this talk, we provide 
several counterexamples to this conjecture with diameter 4 and larger, but we also prove 
the conjecture for several families of distance-regular graphs.

This is joint work with Sebastian M. Cioab\u{a} (University of Delaware), 
Ferdinand Ihringer (Ghent University), and Hirotake Kurihara (Yamaguchi University).


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