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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Optimization Letters
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Laurent, M., & Tanigawa, S.-I. (2017). Perfect elimination orderings for symmetric matrices. Optimization Letters, 14, 339–353. doi:10.1007/s11590-017-1213-y