Isometric Diamond Subgraphs

TL;DR

This paper presents polynomial time algorithms to identify graphs that can be embedded into specific geometric structures like hexagonal tilings and diamond lattices, expanding understanding of partial cube subclasses.

Contribution

Introduces efficient algorithms for recognizing graphs embeddable into certain geometric structures, highlighting a new subclass of partial cubes.

Findings

Algorithms run in polynomial time.

Graphs embeddable in these structures form a distinct subclass of partial cubes.

Provides a method to identify such graphs efficiently.

Abstract

We describe polynomial time algorithms for determining whether an undirected graph may be embedded in a distance-preserving way into the hexagonal tiling of the plane, the diamond structure in three dimensions, or analogous structures in higher dimensions. The graphs that may be embedded in this way form an interesting subclass of the partial cubes.