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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Dan P. Guralnik
Mechanical & Aerospace Engineering, University of Florida, MAE-B, room 327A, 633 Gale Lemerand Dr, Gainesville, FL 32603, USA.
Electrical & Electronics Engineering

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Edge erasures and chordal graphs Jared Culbertson; Dan P. Guralnik; Peter F. Stiller
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.2.13

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.
Co-Authors Jared Culbertson Peter F. Stiller