Proof of the Erd\H{o}s-Simonovits conjecture on walks

Grigoriy Blekherman; Annie Raymond

Proof of the Erd\H{o}s-Simonovits conjecture on walks

Combinatorics 2020-09-24 v1

Authors: Grigoriy Blekherman , Annie Raymond

Abstract

Let $G^n$ be a graph on $n$ vertices and let $w_k(G^n)$ denote the number of walks of length $k$ in $G^n$ divided by $n$ . Erd\H{o}s and Simonovits conjectured that $w_k(G^n)^t \geq w_t(G^n)^k$ when $k\geq t$ and both $t$ and $k$ are odd. We prove this conjecture.

Keywords

graph theory walks Erdős-Simonovits conjecture inequalities

Cite

@article{arxiv.2009.10845,
  title  = {Proof of the Erd\H{o}s-Simonovits conjecture on walks},
  author = {Grigoriy Blekherman and Annie Raymond},
  journal= {arXiv preprint arXiv:2009.10845},
  year   = {2020}
}

Comments

4 pages

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