On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph

Amotz Bar-Noy; Toni Böhnlein; David Peleg; Dror Rawitz

doi:10.4230/LIPIcs.MFCS.2022.14

On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph

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

Bar-Ilan University - The Alexander Kofkin Faculty of Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

4 Scopus citations

Abstract

We consider the problem of characterizing degree sequences that can be realized by a bipartite graph. If a partition of the sequence into the two sides of the bipartite graph is given as part of the input, then a complete characterization has been established over 60 years ago. However, the general question, in which a partition and a realizing graph need to be determined, is still open. We investigate the role of an important class of special partitions, called High-Low partitions, which separate the degrees of a sequence into two groups, the high degrees and the low degrees. We show that when the High-Low partition exists and satisfies some natural properties, analysing the High-Low partition resolves the bigraphic realization problem. For sequences that are known to be not realizable by a bipartite graph or that are undecided, we provide approximate realizations based on the High-Low partition.

Original language	English
Title of host publication	47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022
Editors	Stefan Szeider, Robert Ganian, Alexandra Silva
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)	9783959772563
DOIs	https://doi.org/10.4230/LIPIcs.MFCS.2022.14
State	Published - 1 Aug 2022
Event	47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022 - Vienna, Austria Duration: 22 Aug 2022 → 26 Aug 2022

Publication series

Name	Leibniz International Proceedings in Informatics, LIPIcs
Volume	241
ISSN (Print)	1868-8969

Conference

Conference	47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022
Country/Territory	Austria
City	Vienna
Period	22/08/22 → 26/08/22

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

Approximate Realization
Bigraphic Sequences
Bipartite Graphs
Degree Sequences
Graph Realization
Graphic Sequences
Multigraph Realization

Access to Document

10.4230/LIPIcs.MFCS.2022.14

Cite this

Bar-Noy, A., Böhnlein, T., Peleg, D., & Rawitz, D. (2022). On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph. In S. Szeider, R. Ganian, & A. Silva (Eds.), 47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022 Article 15 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 241). Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.MFCS.2022.14

Bar-Noy, Amotz ; Böhnlein, Toni ; Peleg, David et al. / On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph. 47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022. editor / Stefan Szeider ; Robert Ganian ; Alexandra Silva. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2022. (Leibniz International Proceedings in Informatics, LIPIcs).

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Bar-Noy, A, Böhnlein, T, Peleg, D & Rawitz, D 2022, On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph. in S Szeider, R Ganian & A Silva (eds), 47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022., 15, Leibniz International Proceedings in Informatics, LIPIcs, vol. 241, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022, Vienna, Austria, 22/08/22. https://doi.org/10.4230/LIPIcs.MFCS.2022.14

On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph. / Bar-Noy, Amotz; Böhnlein, Toni; Peleg, David et al.
47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022. ed. / Stefan Szeider; Robert Ganian; Alexandra Silva. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2022. 15 (Leibniz International Proceedings in Informatics, LIPIcs; Vol. 241).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Bar-Noy A, Böhnlein T, Peleg D, Rawitz D. On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph. In Szeider S, Ganian R, Silva A, editors, 47th International Symposium on Mathematical Foundations of Computer Science, MFCS 2022. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2022. 15. (Leibniz International Proceedings in Informatics, LIPIcs). doi: 10.4230/LIPIcs.MFCS.2022.14

On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph

Abstract

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Keywords

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