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On Realizing a Single Degree Sequence by a Bipartite Graph (Invited Paper)

Authors Amotz Bar-Noy, Toni Böhnlein, David Peleg , Dror Rawitz

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Author Details

Amotz Bar-Noy
  • City University of New York (CUNY), NY, USA
Toni Böhnlein
  • Weizmann Institute of Science, Rehovot, Israel
David Peleg
  • Weizmann Institute of Science, Rehovot, Israel
Dror Rawitz
  • Bar Ilan University, Ramat-Gan, Israel

Funding

This work was supported by US-Israel BSF grant 2018043.

Cite AsGet BibTex

Amotz Bar-Noy, Toni Böhnlein, David Peleg, and Dror Rawitz. On Realizing a Single Degree Sequence by a Bipartite Graph (Invited Paper). In 18th Scandinavian Symposium and Workshops on Algorithm Theory (SWAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 227, pp. 1:1-1:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.SWAT.2022.1

Abstract

This paper addresses the classical problem of characterizing degree sequences that can be realized by a bipartite graph. For the simpler variant of the problem, where a partition of the sequence into the two sides of the bipartite graph is given as part of the input, a complete characterization was given by Gale and Ryser over 60 years ago. However, the general question, in which both the partition and the realizing graph need to be determined, is still open. This paper provides an overview of some of the known results on this problem in interesting special cases, including realizations by bipartite graphs and bipartite multigraphs.

Subject Classification

ACM Subject Classification
  • Mathematics of computing → Graph theory
Keywords
  • Degree Sequences
  • Graph Realization
  • Bipartite Graphs
  • Graphic Sequences
  • Bigraphic Sequences
  • Multigraph Realization

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