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arXiv · 2009.07135

How Much Regularity Forces a Sequence to be Graphic?

Brian Cloteaux
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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 $\frac{n-2}{4}$ 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.

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Brian Cloteaux. 2020-09-15. How Much Regularity Forces a Sequence to be Graphic?. https://arxiv.org/abs/2009.07135

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