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Split Graphs: Combinatorial Species and Asymptotics by Troyka, Justin M. is a scholarly article available to read on EtoBox.

What is Split Graphs: Combinatorial Species and Asymptotics about?

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.

Author

Troyka, Justin M.

Published

2018

Language

EN