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Perfect elimination orderings for symmetric matrices

Laurent,Monique
; 
Tanigawa,Shin-ichi
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.
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Date
2020-03
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Tilburg University Research Output Collection
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Keywords
chordal graph, perfect elimination ordering, unit interval graph, ultrametric, shortest path metric, robinson matrix
Citation
Laurent, M & Tanigawa, S 2020, 'Perfect elimination orderings for symmetric matrices', Optimization Letters, vol. 14, no. 2, pp. 339-353. https://doi.org/10.1007/s11590-017-1213-y
URI
https://hdl.handle.net/20.500.14602/68458
License
info:eu-repo/semantics/openAccess
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