License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2022.14
URN: urn:nbn:de:0030-drops-168121
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/16812/
Bar-Noy, Amotz ;
Böhnlein, Toni ;
Peleg, David ;
Rawitz, Dror
On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph
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.
BibTeX - Entry
@InProceedings{barnoy_et_al:LIPIcs.MFCS.2022.14,
author = {Bar-Noy, Amotz and B\"{o}hnlein, Toni and Peleg, David and Rawitz, Dror},
title = {{On the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph}},
booktitle = {47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022)},
pages = {14:1--14:15},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-256-3},
ISSN = {1868-8969},
year = {2022},
volume = {241},
editor = {Szeider, Stefan and Ganian, Robert and Silva, Alexandra},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2022/16812},
URN = {urn:nbn:de:0030-drops-168121},
doi = {10.4230/LIPIcs.MFCS.2022.14},
annote = {Keywords: Graph Realization, Bipartite Graphs, Degree Sequences, Graphic Sequences, Bigraphic Sequences, Approximate Realization, Multigraph Realization}
}
Keywords: |
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Graph Realization, Bipartite Graphs, Degree Sequences, Graphic Sequences, Bigraphic Sequences, Approximate Realization, Multigraph Realization |
Collection: |
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47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022) |
Issue Date: |
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2022 |
Date of publication: |
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22.08.2022 |