Sprinkling with random regular graphs
Combinatorics
2024-07-29 v2
Abstract
We conjecture that the distribution of the edge-disjoint union of two random regular graphs on the same vertex set is asymptotically equivalent to a random regular graph of the combined degree, provided it grows as the number of vertices tends to infinity. We verify this conjecture for the cases when the graphs are sufficiently dense or sparse. We also prove an asymptotic formula for the expected number of spanning regular subgraphs in a random regular graph.
Cite
@article{arxiv.2309.00190,
title = {Sprinkling with random regular graphs},
author = {Mikhail Isaev and Brendan D. McKay and Angus Southwell and Maksim Zhukovskii},
journal= {arXiv preprint arXiv:2309.00190},
year = {2024}
}