Proper circular arc graphs as intersection graphs of paths on a grid
Esther Galby, Maria Pia Mazzoleni, Bernard Ries
TL;DR
This paper characterizes proper circular arc graphs that can be represented as intersection graphs of grid paths with at most one bend, using an infinite family of minimal forbidden induced subgraphs.
Contribution
It provides a new characterization of a specific class of graphs through forbidden subgraphs, linking circular arc graphs and grid path intersection representations.
Findings
Characterization via forbidden induced subgraphs
Identification of an infinite family of minimal forbidden subgraphs
Connection between proper circular arc graphs and grid path intersections
Abstract
In this paper we present a characterisation, by an infinite family of minimal forbidden induced subgraphs, of proper circular arc graphs which are intersection graphs of paths on a grid, where each path has at most one bend (turn).
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Taxonomy
TopicsAdvanced Graph Theory Research · Computational Geometry and Mesh Generation · Graph Labeling and Dimension Problems