Graphs of diameter 3 with the minimum number of edges

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

The graph G is called a porcupine, if G{divides}A is a complete graph for some set A, every other vertex has degree one, and its only edge is joined to A. In this paper a conjecture of Bollobás is settled almost completely. Namely, it is proved that if G is a graph on n vertices of diameter 3 with maximum degree D, D > 2.31 {Mathematical expression}, D ≠ (n - 1)/2 and it has the mimimum number of edges, then it is a porcupine.

Original languageEnglish
Pages (from-to)333-337
Number of pages5
JournalGraphs and Combinatorics
Volume6
Issue number4
DOIs
Publication statusPublished - Dec 1990

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Vertex Degree
Graph in graph theory
Maximum Degree
Complete Graph
Divides

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Mathematics(all)

Cite this

Graphs of diameter 3 with the minimum number of edges. / Füredi, Z.

In: Graphs and Combinatorics, Vol. 6, No. 4, 12.1990, p. 333-337.

Research output: Contribution to journalArticle

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