English

An Optimal Realization Algorithm for Bipartite Graphs with Degrees in Prescribed Intervals

Data Structures and Algorithms 2017-08-21 v1 Discrete Mathematics

Abstract

We consider the problem of constructing a bipartite graph whose degrees lie in prescribed intervals. Necessary and sufficient conditions for the existence of such graphs are well-known. However, existing realization algorithms suffer from large running times. In this paper, we present a realization algorithm that constructs an appropriate bipartite graph G=(U,V,E) in O(|U| + |V| + |E|) time, which is asymptotically optimal. In addition, we show that our algorithm produces edge-minimal bipartite graphs and that it can easily be modified to construct edge-maximal graphs.

Keywords

Cite

@article{arxiv.1708.05520,
  title  = {An Optimal Realization Algorithm for Bipartite Graphs with Degrees in Prescribed Intervals},
  author = {Steffen Rechner},
  journal= {arXiv preprint arXiv:1708.05520},
  year   = {2017}
}

Comments

Submitted to the Journal of Discrete Algorithms

R2 v1 2026-06-22T21:17:45.207Z