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Author

G. Ducoffe

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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
Conference Jul 2026

Beyond Trees: The Weighted Center Problem on Gromov Hyperbolic Graphs

The Weighted Center} problem takes as its input a graph $G=(V,E)$ together with a profile $\pi$ such that every vertex $v$ is mapped to some nonnegative multiplicative weight $\pi(v)$. Its output must be some vertex $c$ minimizing $\max\{\pi(v)d_G(c,v) : v \in V\}$. The classic Center problem corresponds to the case wh...

G. Ducoffe · 0 citations

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