On a property of $2$-connected graphs and Dirac's Theorem

Alexandr Kostochka; Ruth Luo; Grace McCourt

On a property of $2$-connected graphs and Dirac's Theorem

Combinatorics 2023-08-25 v2

Authors: Alexandr Kostochka , Ruth Luo , Grace McCourt

Abstract

We refine a property of $2$ -connected graphs described in the classical paper of Dirac from 1952 and use the refined property to somewhat shorten Dirac's proof of the fact that each $2$ -connected $n$ -vertex graph with minimum degree at least $k$ has a cycle of length at least $\min\{n,2k\}$ .

Keywords

2-connected graphs dirac's theorem cycle length minimum degree graph theory

Cite

@article{arxiv.2212.06897,
  title  = {On a property of $2$-connected graphs and Dirac's Theorem},
  author = {Alexandr Kostochka and Ruth Luo and Grace McCourt},
  journal= {arXiv preprint arXiv:2212.06897},
  year   = {2023}
}

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