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math.CO2026
VC-dimension of distance graphs in finite field geometries
Brian McDonald Bakas, Moustapha Diallo, Alex McDonald
We study the VC-dimension of distance graphs of large subsets of vector spaces over finite fields. For , we prove the distance graph of $E\subset \F_q^d$ has VC-dime…
math.CA2026
Extremal graph theory and point configurations in Ahlfors-David regular sets
Alex McDonald
We study the problem of embedding bipartite graphs in Ahlfors-David regular sets of large dimension using results from extremal graph theory. Our main theorem states that any graph…