Length thresholds for graphic lists given fixed largest and smallest entries and bounded gaps

@article{Barrus2012LengthTF,
title={Length thresholds for graphic lists given fixed largest and smallest entries and bounded gaps},
author={Michael D. Barrus and Stephen G. Hartke and Kyle F. Jao and Douglas B. West},
journal={Discrete Mathematics},
year={2012},
volume={312},
pages={1494-1501}
}

In a list (d1, . . . , dn) of positive integers, let r and s denote the largest and smallest entries. A list is gap-free if each integer between r and s is present. We prove that a gapfree even-summed list is graphic if it has at least r + r+s+1 2s terms. With no restriction on gaps, length at least (r+s+1) 2 4s suffices, as proved by Zverovich and Zverovich. Both bounds are sharp within 1. When the gaps between consecutive terms are bounded by g, we prove a more general length threshold that… CONTINUE READING