The Interval function, Ptolemaic, distance hereditary, bridged graphs and axiomatic characterizations
英文摘要：
In this paper we consider certain types of betweenness axioms on the interval function $I_G$ of a connected graph $G$. We characterize the class of graphs for which $I_G$ 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}.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
