Abstract
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.
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