N0 completions on partial matrices

An n×n matrix is called an N0-matrix if all its principal minors are non-positive. In this paper, we are interested in N0-matrix completion problems, that is, when a partial N0-matrix has an N0-matrix completion. In general, a combinatorially or non-combinatorially symmetric partial N0-matrix does not have an N0-matrix completion. Here, we prove that a combinatorially symmetric partial N0-matrix, with no null main diagonal entries, has an N0-matrix completion if the graph of its specified entries is a 1-chordal graph or a cycle. We also analyze the mentioned problem when the partial matrix has some null main diagonal entries.