Graph comparison meets Alexandrov
Nina Lebedeva, Anton Petrunin
TL;DR
This paper explores the relationship between graph comparison conditions and Alexandrov's comparisons, revealing that nontrivial graph comparisons imply Alexandrov's comparisons and characterizing graphs with trivial comparisons.
Contribution
It establishes a connection between graph comparison conditions and Alexandrov's comparisons, providing a complete description of graphs with trivial comparisons.
Findings
Nontrivial graph comparisons imply Alexandrov's comparisons.
Complete characterization of graphs with trivial graph comparisons.
Abstract
Graph comparison is a certain type of condition on metric space encoded by a finite graph. We show that any nontrivial graph comparison implies one of Alexandrov's comparisons. The proof gives a complete description of graphs with trivial graph comparisons.
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Taxonomy
TopicsBioinformatics and Genomic Networks · Graph Theory and Algorithms