Edge Erasures and Chordal Graphs
Combinatorics
2018-08-16 v2 Discrete Mathematics
Geometric Topology
Abstract
We prove several results about chordal graphs and weighted chordal graphs by focusing on exposed edges. These are edges that are properly contained in a single maximal complete subgraph. This leads to a characterization of chordal graphs via deletions of a sequence of exposed edges from a complete graph. Most interesting is that in this context the connected components of the edge-induced subgraph of exposed edges are 2-edge connected. We use this latter fact in the weighted case to give a modified version of Kruskal's second algorithm for finding a minimum spanning tree in a weighted chordal graph. This modified algorithm benefits from being local in an important sense.
Keywords
Cite
@article{arxiv.1706.04537,
title = {Edge Erasures and Chordal Graphs},
author = {Jared Culbertson and Dan P. Guralnik and Peter F. Stiller},
journal= {arXiv preprint arXiv:1706.04537},
year = {2018}
}
Comments
9 pages, 3 figures; minor revisions to enhance clarity