English

How Much Regularity Forces a Sequence to be Graphic?

Combinatorics 2020-09-16 v1

Abstract

For an integer sequence (with even sum), the closer that the sequence is to being regular, the more likely that the sequence is graphic. But how regular must a sequence be before it must always be graphic? We show that for many sequences if all values are within n24\frac{n-2}{4} of the mean degree value, then the sequence is graphic. We also see how this result extends to show when a maximum difference between sequence values implies that a sequence is graphic.

Cite

@article{arxiv.2009.07135,
  title  = {How Much Regularity Forces a Sequence to be Graphic?},
  author = {Brian Cloteaux},
  journal= {arXiv preprint arXiv:2009.07135},
  year   = {2020}
}
R2 v1 2026-06-23T18:33:36.120Z