The Interval function, Ptolemaic, distance hereditary, bridged graphs and axiomatic characterizations
Discrete Mathematics
2020-05-15 v1 Combinatorics
Abstract
In this paper we consider certain types of betweenness axioms on the interval function of a connected graph . We characterize the class of graphs for which satisfy these axioms. The class of graphs that we characterize include the important class of Ptolemaic graphs and some proper superclasses of Ptolemaic graphs: the distance hereditary graphs and the bridged graphs. We also provide axiomatic characterizations of the interval function of these classes of graphs using an arbitrary function known as \emph{transit function}.
Keywords
Cite
@article{arxiv.2005.06751,
title = {The Interval function, Ptolemaic, distance hereditary, bridged graphs and axiomatic characterizations},
author = {Manoj Changat and Lekshmi Kamal K. Sheela and Prasanth G. Narasimha-Shenoi},
journal= {arXiv preprint arXiv:2005.06751},
year = {2020}
}