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 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}
}