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On the Number of Shortest Paths in Graphs

2023/11/16 by Itaï Benjamini, Benjamini, Itai, Elad Tzalik +1
Computer Science · Mathematics · #Advanced Graph Theory Research #Limits and Structures in Graph Theory #Graph Labeling and Dimension Problems

paper · pdf · doi:10.48550/arxiv.2311.10014

Abstract

It is proved that the number of shortest paths between two vertices of distance t in a graph with degrees bounded by Δ is at most 2 ⋅ (\fracΔ2)t. This improves upon the naïve Δ(Δ-1) t-1 bound.

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