Author

Bogdan C. Dumitru

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Preprint Sep 2026

Towards a more structured search for Erd\H{o}s-Gy\'arf\'as counter-examples

The Erd\H{o}s-Gy\'arf\'as conjecture posits that every graph with minimum degree at least three contains a cycle of length some power of two. We prove a few simple structural properties for any minimal counter-example to this conjecture. In particular, the fraction of its vertices of degree three must be greater than $...

G. Ducoffe, Bogdan C. Dumitru · 0 citations

Preprint Sep 2026

Short arithmetic terms for the cardinality of elliptic curves over rings of remainder classes and over finite fields

Arithmetic terms are fixed finite compositions of addition, truncated subtraction, multiplication, integer division and exponentiation on natural numbers. We construct such terms for the number of affine solutions of $ y^2 = x^3 + Ax + B $. For arbitrary moduli $ n \geq 1 $, a specialization of Prunescu's general const...

Bogdan C. Dumitru, Mihai Prunescu · 0 citations