Graphs with degree constraints
Combinatorics
2015-07-22 v2
Abstract
Given a set D of nonnegative integers, we derive the asymptotic number of graphs with a givenvnumber of vertices, edges, and such that the degree of every vertex is in D. This generalizes existing results, such as the enumeration of graphs with a given minimum degree, and establishes new ones, such as the enumeration of Euler graphs, i.e. where all vertices have an even degree. Those results are derived using analytic combinatorics.
Keywords
Cite
@article{arxiv.1506.03061,
title = {Graphs with degree constraints},
author = {Élie de Panafieu and Lander Ramos},
journal= {arXiv preprint arXiv:1506.03061},
year = {2015}
}
Comments
10 pages, 7 pages of appendix, 1 figure