Hypercube Subgraphs with Minimal Detours

Pál Erdös, Peter Hamburger, Raymond E. Pippert, William D. Weakley

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Define a minimal detour subgraph of the n-dimensional cube to be a spanning subgraph G of Qn having the property that for vertices x, y of Qn, distances are related by dG(x, y) ≤ dQn(x, y) + 2. Let f(n) be the minimum number of edges of such a subgraph of Qn. After preliminary work on distances in subgraphs of product graphs, we show that f(n)/|E(Qn| < c/√n. The subgraphs we construct to establish this bound have the property that the longest distances are the same as in Qn, and thus the diameter does not increase. We establish a lower bound for f(n), show that vertices of high degree must be distributed throughout a minimal detour subgraph of Qn, and end with conjectures and questions.

Original languageEnglish
Pages (from-to)119-128
Number of pages10
JournalJournal of Graph Theory
Volume23
Issue number2
DOIs
Publication statusPublished - Oct 1996

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ASJC Scopus subject areas

  • Geometry and Topology

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