On central max-point-tolerance graphs

Abstract

Max-point-tolerance graphs (MPTG) were studied by Catanzaro et al. in 2017 and the same class of graphs were introduced in the name of p-BOX(1) graphs by Soto and Caro in 2015. This class has a wide application in genome studies as well as in telecommunication networks. In our article, we consider central max-point-tolerance graphs (central MPTG) by taking the points of MPTG as center points of their corresponding intervals. In the course of study on this class of graphs, we show that the class of central MPTG is same as the class of unit max-tolerance graphs. We also prove that the class of unit central MPTG is same as that of proper central MPTG and both of them are equivalent to the class of proper interval graphs.

Keywords

• interval graph
• proper interval graph
• tolerance graph
• max-tolerance graph
• max-point-tolerance graph