English

Every graph contains a linearly sized induced subgraph with all degrees odd

Combinatorics 2021-04-02 v3

Abstract

We prove that every graph GG on nn vertices with no isolated vertices contains an induced subgraph of size at least n/10000n/10000 with all degrees odd. This solves an old and well-known conjecture in graph theory.

Keywords

Cite

@article{arxiv.2009.05495,
  title  = {Every graph contains a linearly sized induced subgraph with all degrees odd},
  author = {Asaf Ferber and Michael Krivelevich},
  journal= {arXiv preprint arXiv:2009.05495},
  year   = {2021}
}
R2 v1 2026-06-23T18:28:39.029Z