Planar L-Drawings of Bimodal Graphs

TL;DR

This paper investigates planar L-drawings of bimodal graphs, proving that all plane bimodal graphs without 2-cycles and all outerplanar digraphs can be represented with such drawings, expanding understanding of graph visualization.

Contribution

It establishes that every plane bimodal graph without 2-cycles admits a planar L-drawing, including upward-plane graphs, and shows outerplanar digraphs can also be drawn this way.

Findings

All plane bimodal graphs without 2-cycles admit planar L-drawings.

Outerplanar digraphs can be represented with planar L-drawings.

Not all outerplanar digraphs have an outerplanar embedding with an L-drawing.

Abstract

In a planar L-drawing of a directed graph (digraph) each edge e is represented as a polyline composed of a vertical segment starting at the tail of e and a horizontal segment ending at the head of e. Distinct edges may overlap, but not cross. Our main focus is on bimodal graphs, i.e., digraphs admitting a planar embedding in which the incoming and outgoing edges around each vertex are contiguous. We show that every plane bimodal graph without 2-cycles admits a planar L-drawing. This includes the class of upward-plane graphs. Finally, outerplanar digraphs admit a planar L-drawing - although they do not always have a bimodal embedding - but not necessarily with an outerplanar embedding.