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.

Chordal graph, Perfect elimination ordering, Robinson matrix, Shortest path metric, Ultrametric, Unit interval graph
Optimization Letters
Centrum Wiskunde & Informatica, Amsterdam, The Netherlands

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