Symmetric completions of cycles and bipartite graphs

The analysis of symmetric completions of partial matrices associated with a simple graph G, in terms of inertias and minimal rank, simplifies dramatically when G is bipartite. Essentially, it is equivalent to the analysis of an associated non-symmetric completion problem. All the inertias down to th...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 614; pp. 164 - 175
Main Authors Cohen, Nir, Pereira, Edgar
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.04.2021
American Elsevier Company, Inc
Subjects
Chordal
Codes
Cyclic graph
Graphs
Linear algebra
Mathematical analysis
Matrix methods
Rank completion
Symmetric partial matrix
Rank completion
05C50
15A21
Cyclic graph
16G20
Chordal
Symmetric partial matrix
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Summary:The analysis of symmetric completions of partial matrices associated with a simple graph G, in terms of inertias and minimal rank, simplifies dramatically when G is bipartite. Essentially, it is equivalent to the analysis of an associated non-symmetric completion problem. All the inertias down to the minimum rank can be obtained, but the minimal rank itself remains NP-hard for general graphs in this class. The class of bipartite graphs includes even cycles but excludes odd cycles. By the above reduction we provide relatively sharp minimal rank estimates for even cycles and discuss some counter-examples raised by odd cycles.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2020.03.029