On central-max-point tolerance graphs and some subclasses of interval catch digraphs
Sanchita Paul, Shamik Ghosh

TL;DR
This paper explores various subclasses of interval catch digraphs and max-point-tolerance graphs, establishing equivalences, disproving conjectures, and characterizing these graphs through forbidden subdigraphs and matrix properties.
Contribution
It introduces and characterizes central-max-point tolerance graphs, disproves a conjecture on central ICDs, and relates these classes to proper interval graphs and other digraphs.
Findings
Central MPTG is equivalent to unit max-tolerance graphs.
Proper central MPTG and proper interval graphs are equivalent.
Disproved Maehera's conjecture on central ICD characterization.
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. In our paper we consider central-max-point tolerance graphs (central MPTG) by taking the points of MPTG as center points of their corresponding intervals. In 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 prove the class of unit central max-point tolerance graphs is same as that of proper central max-point tolerance graphs and both of them are equivalent to the class of proper interval graphs. Next we introduce 50% max-tolerance graphs and separate this class from unit max-tolerance graph whereas for min-tolerance graphs 50% and unit denote the same graph class. Interval catch digraphs (ICD) was introduced by Maehera in 1984.…
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Taxonomy
TopicsAdvanced Graph Theory Research · Interconnection Networks and Systems · Graph Labeling and Dimension Problems
