Some Properties of Yao Y4 Subgraphs

TL;DR

This paper investigates the properties of Yao Y4 subgraphs, focusing on planarity, connectedness, and spanner properties, revealing differences among subgraphs based on their quadrant partitioning.

Contribution

It provides new insights into the structural properties of Yao Y4 subgraphs, highlighting differences across quadrants in planarity, connectivity, and spanner characteristics.

Findings

Subgraphs in one quadrant differ from those in two adjacent quadrants in planarity.

Connectivity varies among subgraphs across different quadrants.

Spanner properties are not uniform across all Yao Y4 subgraphs.

Abstract

The Yao graph for k=4, Y4, is naturally partitioned into four subgraphs, one per quadrant. We show that the subgraphs for one quadrant differ from the subgraphs for two adjacent quadrants in three properties: planarity, connectedness, and whether the directed graphs are spanners.