Largest non-unique subgraphs

Lars Døvling Andersen, Preben Dahl Vestergaard, Z. Tuza

Research output: Contribution to journalArticle

Abstract

The reduction number r(G) of a graph G is the maximum integer m≤|E(G)| such that the graphs G-E, ⊆E(G),|E|≤m, are mutually non-isomorphic, i.e., each graph is unique as a subgraph of G. We prove that [InlineMediaObject not available: see fulltext.] and show by probabilistic methods that r(G) can come close to this bound for large orders. By direct construction, we exhibit graphs with large reduction number, although somewhat smaller than the upper bound. We also discuss similarities to a parameter introduced by Erdos and Rényi capturing the degree of asymmetry of a graph, and we consider graphs with few circuits in some detail.

Original languageEnglish
Pages (from-to)453-470
Number of pages18
JournalGraphs and Combinatorics
Volume22
Issue number4
DOIs
Publication statusPublished - Dec 2006

Fingerprint

Subgraph
Graph in graph theory
Reduction number
Networks (circuits)
Probabilistic Methods
Erdös
Asymmetry
Upper bound
Integer

Keywords

  • Asymmetry
  • Edge deletion
  • Isomorphism
  • Random graph
  • Reduction number
  • Spanning subgraph
  • Symmetry
  • Tree
  • Unicyclic graph
  • Unique subgraph

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics

Cite this

Largest non-unique subgraphs. / Andersen, Lars Døvling; Vestergaard, Preben Dahl; Tuza, Z.

In: Graphs and Combinatorics, Vol. 22, No. 4, 12.2006, p. 453-470.

Research output: Contribution to journalArticle

Andersen, LD, Vestergaard, PD & Tuza, Z 2006, 'Largest non-unique subgraphs', Graphs and Combinatorics, vol. 22, no. 4, pp. 453-470. https://doi.org/10.1007/s00373-006-0676-x
Andersen, Lars Døvling ; Vestergaard, Preben Dahl ; Tuza, Z. / Largest non-unique subgraphs. In: Graphs and Combinatorics. 2006 ; Vol. 22, No. 4. pp. 453-470.
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