Perfect Elimination Orderings for Symmetric Matrices
Combinatorics
2018-11-20 v1
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.
Cite
@article{arxiv.1704.05115,
title = {Perfect Elimination Orderings for Symmetric Matrices},
author = {Monique Laurent and Shin-ichi Tanigawa},
journal= {arXiv preprint arXiv:1704.05115},
year = {2018}
}
Comments
16 pages, 3 figures