TL;DR
This paper presents a polynomial time algorithm to determine the smallest lattice dimension into which a given graph can be isometrically embedded, advancing understanding of graph embeddings in lattice structures.
Contribution
It introduces the first polynomial time algorithm for finding the minimum lattice dimension for isometric graph embedding.
Findings
Algorithm runs in polynomial time
Determines minimal lattice dimension for any graph
Enhances methods for graph embedding analysis
Abstract
We describe a polynomial time algorithm for, given an undirected graph G, finding the minimum dimension d such that G may be isometrically embedded into the d-dimensional integer lattice Z^d.
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