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.
| Original language | English |
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| Title of host publication | 18th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2022 |
| Editors | Artur Czumaj, Qin Xin |
| Publisher | Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing |
| ISBN (Electronic) | 9783959772365 |
| DOIs | |
| State | Published - 1 Jun 2022 |
| Event | 18th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2022 - Torshavn, Faroe Islands Duration: 27 Jun 2022 → 29 Jun 2022 |
Publication series
| Name | Leibniz International Proceedings in Informatics, LIPIcs |
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| Volume | 227 |
| ISSN (Print) | 1868-8969 |
Conference
| Conference | 18th Scandinavian Symposium and Workshops on Algorithm Theory, SWAT 2022 |
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| Country/Territory | Faroe Islands |
| City | Torshavn |
| Period | 27/06/22 → 29/06/22 |
Bibliographical note
Publisher Copyright:© 2022 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.
Funding
This work was supported by US-Israel BSF grant 2018043.
| Funders | Funder number |
|---|---|
| US-Israel BSF | 2018043 |
Keywords
- Bigraphic Sequences
- Bipartite Graphs
- Degree Sequences
- Graph Realization
- Graphic Sequences
- Multigraph Realization