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

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 the Role of the High-Low Partition in Realizing a Degree Sequence by a Bipartite Graph. In 47th International Symposium on Mathematical Foundations of Computer Science (MFCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 241, pp. 14:1-14:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)
https://doi.org/10.4230/LIPIcs.MFCS.2022.14

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.

Subject Classification

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

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