Hypercube Subgraphs with Minimal Detours

P. Erdős, 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
Publication statusPublished - Oct 1996

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Hypercube
Subgraph
Product Graph
Cube
Spanning Subgraph
n-dimensional
Lower bound

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Erdős, P., Hamburger, P., Pippert, R. E., & Weakley, W. D. (1996). Hypercube Subgraphs with Minimal Detours. Journal of Graph Theory, 23(2), 119-128.

Hypercube Subgraphs with Minimal Detours. / Erdős, P.; Hamburger, Peter; Pippert, Raymond E.; Weakley, William D.

In: Journal of Graph Theory, Vol. 23, No. 2, 10.1996, p. 119-128.

Research output: Contribution to journalArticle

Erdős, P, Hamburger, P, Pippert, RE & Weakley, WD 1996, 'Hypercube Subgraphs with Minimal Detours', Journal of Graph Theory, vol. 23, no. 2, pp. 119-128.
Erdős P, Hamburger P, Pippert RE, Weakley WD. Hypercube Subgraphs with Minimal Detours. Journal of Graph Theory. 1996 Oct;23(2):119-128.
Erdős, P. ; Hamburger, Peter ; Pippert, Raymond E. ; Weakley, William D. / Hypercube Subgraphs with Minimal Detours. In: Journal of Graph Theory. 1996 ; Vol. 23, No. 2. pp. 119-128.
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