Global cycle properties in locally isometric graphs
Combinatorics
2016-01-08 v2
Abstract
A graph G is locally isometric if the subgraph induced by the neighbourhood of every vertex is an isometric subgraph of G. It is shown that the hamilton cycle problem for locally isometric graphs with maximum degree at most 8 is NP-complete. Structural characterizations of locally isometric graphs, with maximum degree at most 6, that are fully cycle extendable, are established and these results are used to show that locally isometric graphs with maximum degree at most 6 are weakly pancyclic. This proves Ryjacek's conjecture for a subclass of locally connected graphs.
Keywords
Cite
@article{arxiv.1506.03310,
title = {Global cycle properties in locally isometric graphs},
author = {Adam Borchert and Skylar Nicol and Ortrud R. Oellermann},
journal= {arXiv preprint arXiv:1506.03310},
year = {2016}
}
Comments
13 pages three figures