dc.contributor.author | Ter Horst, S. | |
dc.contributor.author | Klem, E.M. | |
dc.date.accessioned | 2017-03-20T08:25:28Z | |
dc.date.available | 2017-03-20T08:25:28Z | |
dc.date.issued | 2017 | |
dc.identifier.citation | Ter Horst, S. & Klem, E.M. 2017. Graphs with sparsity order at most two: the complex case. Linear and multilinear algebra, 65(12):2367-2386. [http://dx.doi.org/10.1080/03081087.2016.1274362] | en_US |
dc.identifier.issn | 0308-1087 | |
dc.identifier.issn | 1563-5139 (Online) | |
dc.identifier.uri | http://hdl.handle.net/10394/20885 | |
dc.identifier.uri | http://dx.doi.org/10.1080/03081087.2016.1274362 | |
dc.identifier.uri | http://www.tandfonline.com/doi/full/10.1080/03081087.2016.1274362 | |
dc.description.abstract | The sparsity order of a (simple undirected) graph is the highest possible rank (over
or
) of the extremal elements in the matrix cone that consists of positive semidefinite matrices with prescribed zeros on the positions that correspond to non-edges of the graph (excluding the diagonal entries). The graphs of sparsity order 1 (for both
and
) correspond to chordal graphs, those graphs that do not contain a cycle of length greater than three, as an induced subgraph, or equivalently, is a clique-sum of cliques. There exist analogues, though more complicated, characterizations of the case where the sparsity order is at most 2, which are different for
and
. The existing proof for the complex case, is based on the result for the real case. In this paper we provide a more elementary proof of the characterization of the graphs whose complex sparsity order is at most two. Part of our proof relies on a characterization of the
-free graphs, with
the path of length 3 and
the stable set of cardinality 3, and of the class of clique-sums of such graphs | en_US |
dc.language.iso | en | en_US |
dc.publisher | Taylor & Francis | en_US |
dc.subject | Sparsity order | en_US |
dc.subject | Matrix cones | en_US |
dc.subject | Forbidden subgraphs | en_US |
dc.title | Graphs with sparsity order at most two: the complex case | en_US |
dc.type | Article | en_US |
dc.contributor.researchID | 24116327 - Ter Horst, Sanne | |