How to decrease the diameter of triangle-free graphs

P. Erdős, A. Gyárfás, Miklós Ruszinkó

Research output: Contribution to journalArticle

24 Citations (Scopus)

Abstract

Assume that G is a triangle-free graph. Let hd(G) be the minimum number of edges one has to add to G to get a graph of diameter at most d which is still triangle-free. It is shown that h2(G) = θ(n log n) for connected graphs of order n and of fixed maximum degree. The proof is based on relations of h2(G) and the clique-cover number of edges of graphs. It is also shown that the maximum value of h2(G) over (triangle-free) graphs of order n is ⌈n/2 - 1⌉⌊n/2 - 1⌋. The behavior of h3(G) is different, its maximum value is n - 1. We could not decide whether h4(G)≤(1 - ∈)n for connected (triangle-free) graphs of order n with a positive ∈.

Original languageEnglish
Pages (from-to)493-501
Number of pages9
JournalCombinatorica
Volume18
Issue number4
Publication statusPublished - 1998

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Triangle-free Graph
Decrease
Connected graph
Triangle-free
Graph in graph theory
Clique
Maximum Degree
Cover

ASJC Scopus subject areas

  • Mathematics(all)
  • Discrete Mathematics and Combinatorics

Cite this

How to decrease the diameter of triangle-free graphs. / Erdős, P.; Gyárfás, A.; Ruszinkó, Miklós.

In: Combinatorica, Vol. 18, No. 4, 1998, p. 493-501.

Research output: Contribution to journalArticle

Erdős, P. ; Gyárfás, A. ; Ruszinkó, Miklós. / How to decrease the diameter of triangle-free graphs. In: Combinatorica. 1998 ; Vol. 18, No. 4. pp. 493-501.
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