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L-Graphs and Monotone L-Graphs
- Publication Year :
- 2017
-
Abstract
- In an $\mathsf{L}$-embedding of a graph, each vertex is represented by an $\mathsf{L}$-segment, and two segments intersect each other if and only if the corresponding vertices are adjacent in the graph. If the corner of each $\mathsf{L}$-segment in an $\mathsf{L}$-embedding lies on a straight line, we call it a monotone $\mathsf{L}$-embedding. In this paper we give a full characterization of monotone $\mathsf{L}$-embeddings by introducing a new class of graphs which we call "non-jumping" graphs. We show that a graph admits a monotone $\mathsf{L}$-embedding if and only if the graph is a non-jumping graph. Further, we show that outerplanar graphs, convex bipartite graphs, interval graphs, 3-leaf power graphs, and complete graphs are subclasses of non-jumping graphs. Finally, we show that distance-hereditary graphs and $k$-leaf power graphs ($k\le 4$) admit $\mathsf{L}$-embeddings.
- Subjects :
- Computer Science - Computational Geometry
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1703.01544
- Document Type :
- Working Paper