Bounds for minimum semidefinite rank from superpositions and cutsets

DOI10.1016/j.laa.2012.07.012zbMath1282.05094OpenAlexW1970394054MaRDI QIDQ389675

Jonathan E. Beagley, Sivaram K. Narayan, Sara P. Rimer, Andrew M. Zimmer, Lon H. Mitchell, Rachael L. Tomasino, Jennifer L. Wolfe, Eileen L. Radzwion

Publication date: 21 January 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2012.07.012

zbMATH Keywords

minimum semidefinite rankcutsetssuperposition of graphsvector representation of a graph

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Graph representations (geometric and intersection representations, etc.) (05C62)

Related Items (3)

The minimum semidefinite rank of a triangle-free graph ⋮ Positive semidefinite zero forcing numbers of two classes of graphs ⋮ Lower bounds in minimum rank problems

Cites Work

• Vector representations of graphs
• Linearly independent vertices and minimum semidefinite rank
• Zero forcing parameters and minimum rank problems
• The minimum rank of symmetric matrices described by a graph: a survey
• Lower bounds in minimum rank problems
• Graphs whose positive semi-definite matrices have nullity at most two
• Zero forcing sets and the minimum rank of graphs
• On the minimum semidefinite rank of a simple graph
• On the maximum positive semi-definite nullity and the cycle matroid of graphs
• Graphs whose minimal rank is two
• A Property of 4-Chromatic Graphs and some Remarks on Critical Graphs

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