English

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

R2 v1 2026-06-22T09:50:29.093Z