NeST graphs

Authors:
Ryan B. Hayward;Paul E. Kearney;Andrew Malton
Affiliations:
Department of Computing Science, University of Alberta, Edmonton, Alberta, Canada T6G 2E1;Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1;Department of Computer Science, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1
Venue:
Discrete Applied Mathematics
Year:
2002

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Abstract

We establish results on NeST graphs (intersection tolerance graphs of neighborhood subtrees of a tree) and several subclasses. In particular, we show the equivalence of proper NeST graphs and unit NeST graphs, the equivalence of fixed distance NeST graphs and threshold tolerance graphs, and the proper containment of NeST graphs in weakly chordal graphs. The latter two results answer questions of Monma, Reed and Trotter, and Bibelnieks and Dearing.