A Note on Diameter Certification in Trees

Josef Erik Sedláček

A Note on Diameter Certification in Trees

Distributed, Parallel, and Cluster Computing 2026-07-10 v1

Authors: Josef Erik Sedláček

Abstract

In the local certification model, certifying the diameter of general graphs requires large certificates, but trees admit more efficient solutions. In this note, we provide a $1$ -local certification scheme that certifies whether the diameter of a given tree is at most $d$ using certificates of at most $3\lceil\log_2(d+1)\rceil$ bits.

Cite

@article{arxiv.2607.09929,
  title  = {A Note on Diameter Certification in Trees},
  author = {Josef Erik Sedláček},
  journal= {arXiv preprint arXiv:2607.09929},
  year   = {2026}
}

Comments

5 pages, no figures