English

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.

Keywords

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

R2 v1 2026-06-22T19:19:28.333Z