On some simplicial elimination schemes for chordal graphs

TL;DR

This paper explores specific elimination schemes for chordal graphs, demonstrating that a linear-time construction of a simplicial elimination scheme is possible starting from a particular maximal clique connected through a minimal separator.

Contribution

It introduces a linear-time method to construct simplicial elimination schemes for chordal graphs based on particular maximal cliques and minimal separators.

Findings

Linear-time construction of elimination schemes

Identification of specific maximal cliques and minimal separators

Efficient algorithms for chordal graph processing

Abstract

We present here some results on particular elimination schemes for chordal graphs, namely we show that for any chordal graph we can construct in linear time a simplicial elimination scheme starting with a pending maximal clique attached via a minimal separator maximal (resp. minimal) under inclusion among all minimal separators.