Perfect Elimination Orderings for Symmetric Matrices

Monique Laurent, Shin-ichi Tanigawa

Research output: Working paperOther research output

Abstract

We introduce a new class of structured symmetric matrices by extending the notion of perfect elimination ordering from graphs to weighted graphs or matrices. This offers a common framework capturing common vertex elimination orderings of monotone families of chordal graphs, Robinsonian matrices and ultrametrics. We give a structural characterization for matrices that admit perfect elimination orderings in terms of forbidden substructures generalizing chordless cycles in graphs.
Original languageEnglish
Place of PublicationIthaca
PublisherCornell University Library
Number of pages17
Publication statusPublished - 17 Apr 2017

Publication series

NamearXiv
Volume1706.05115

Fingerprint

Symmetric matrix
Elimination
Structured Matrices
Chordal Graphs
Weighted Graph
Substructure
Graph in graph theory
Monotone
Cycle
Vertex of a graph

Keywords

  • Chordal graph
  • Perfect elimination ordering
  • Unit interval
  • Ultrametric
  • Shortest path metric
  • Robinson matrix

Cite this

Laurent, M., & Tanigawa, S. (2017). Perfect Elimination Orderings for Symmetric Matrices. (arXiv; Vol. 1706.05115). Ithaca: Cornell University Library.
Laurent, Monique ; Tanigawa, Shin-ichi. / Perfect Elimination Orderings for Symmetric Matrices. Ithaca : Cornell University Library, 2017. (arXiv).
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Laurent, M & Tanigawa, S 2017 'Perfect Elimination Orderings for Symmetric Matrices' arXiv, vol. 1706.05115, Cornell University Library, Ithaca.

Perfect Elimination Orderings for Symmetric Matrices. / Laurent, Monique; Tanigawa, Shin-ichi.

Ithaca : Cornell University Library, 2017. (arXiv; Vol. 1706.05115).

Research output: Working paperOther research output

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KW - Unit interval

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KW - Shortest path metric

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Laurent M, Tanigawa S. Perfect Elimination Orderings for Symmetric Matrices. Ithaca: Cornell University Library. 2017 Apr 17. (arXiv).