Monotone Drawings of $k$-Inner Planar Graphs
Anargyros Oikonomou, Antonios Symvonis

TL;DR
This paper presents a method to construct monotone drawings of $k$-inner planar graphs on polynomial-sized grids, with improved results for outerplanar graphs, enhancing visualization techniques for these graph classes.
Contribution
The paper introduces a new construction method for monotone drawings of $k$-inner planar graphs on polynomial grids, improving existing results for outerplanar graphs.
Findings
Monotone drawings of $k$-inner planar graphs can be achieved on a $2(k+1)n imes 2(k+1)n$ grid.
Outerplanar graphs admit planar monotone drawings on an $n imes n$ grid, improving previous bounds.
The method enhances graph visualization by providing efficient grid drawings for these classes.
Abstract
A -inner planar graph is a planar graph that has a plane drawing with at most {internal vertices}, i.e., vertices that do not lie on the boundary of the outer face of its drawing. An outerplanar graph is a -inner planar graph. In this paper, we show how to construct a monotone drawing of a -inner planar graph on a grid. In the special case of an outerplanar graph, we can produce a planar monotone drawing on a grid, improving previously known results.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Interactive and Immersive Displays · QR Code Applications and Technologies
