On Realizing a Single Degree Sequence by a Bipartite Graph (Invited Paper)
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.
Degree Sequences
Graph Realization
Bipartite Graphs
Graphic Sequences
Bigraphic Sequences
Multigraph Realization
Mathematics of computing~Graph theory
1:1-1:17
Invited Paper
This work was supported by US-Israel BSF grant 2018043.
Amotz
Bar-Noy
Amotz Bar-Noy
City University of New York (CUNY), NY, USA
Toni
Böhnlein
Toni Böhnlein
Weizmann Institute of Science, Rehovot, Israel
David
Peleg
David Peleg
Weizmann Institute of Science, Rehovot, Israel
https://orcid.org/0000-0003-1590-0506
Dror
Rawitz
Dror Rawitz
Bar Ilan University, Ramat-Gan, Israel
10.4230/LIPIcs.SWAT.2022.1
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Amotz Bar-Noy, Toni Böhnlein, David Peleg, and Dror Rawitz
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