Triple crossing numbers of graphs
Hiroyuki Tanaka, Masakazu Teragaito
TL;DR
This paper introduces the triple crossing number, a new graph invariant measuring the minimal number of triple crossings in a drawing, and determines this number for all complete multipartite graphs including complete graphs.
Contribution
It defines the triple crossing number and computes it explicitly for all complete multipartite graphs, expanding understanding of graph crossing properties.
Findings
Triple crossing number is zero for planar graphs.
Triple crossing number is infinite for graphs without triple crossing drawings.
Explicit values of triple crossing numbers for all complete multipartite graphs.
Abstract
We introduce the triple crossing number, a variation of crossing number, of a graph, which is the minimal number of crossing points in all drawings with only triple crossings of the graph. It is defined to be zero for a planar graph, and to be infinite unless a graph admits a drawing with only triple crossings. In this paper, we determine the triple crossing numbers for all complete multipartite graphs including all complete graphs.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsComputational Geometry and Mesh Generation · Remote Sensing and LiDAR Applications · Advanced Graph Theory Research