Split graphs: combinatorial species and asymptotics
Combinatorics
2019-07-16 v3
Abstract
A split graph is a graph whose vertices can be partitioned into a clique and a stable set. We investigate the combinatorial species of split graphs, providing species-theoretic generalizations of enumerative results due to B\'ina and P\v{r}ibil (2015), Cheng, Collins, and Trenk (2016), and Collins and Trenk (2018). In both the labeled and unlabeled cases, we give asymptotic results on the number of split graphs, of unbalanced split graphs, and of bicolored graphs, including proving the conjecture of Cheng, Collins, and Trenk (2016) that almost all split graphs are balanced.
Cite
@article{arxiv.1803.07248,
title = {Split graphs: combinatorial species and asymptotics},
author = {Justin M. Troyka},
journal= {arXiv preprint arXiv:1803.07248},
year = {2019}
}
Comments
18 pages; to appear in Electron. J. Combin.; Section 4 has been removed because it proves a theorem that has been found in the literature since the previous version