How to make a random graph irregular

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

An irregular edge labeling of a graph G = (V, E) is a weight assignment f: E→ N such that the sums f + (v):= Σv∈e∈E f(e) are pairwise distinct. If such labelings exist in G, then the value of minf Σe∈E (f(e) ‐ 1) measures the minimum number of edges needed to make G irregular. We prove that this minimum for the random graph G(n, p) with n vertices and edge probability p = p(n) is equal to n2/4 + o(n2) as n→∞, whenever p(n)‐n2/3→∞. This asymptotic result is deduced from a general estimate (valid for every graph) involving vertex degrees and the size of largest triangle packings. © 1995 John Wiley & Sons, Inc.

Original languageEnglish
Pages (from-to)323-329
Number of pages7
JournalRandom Structures & Algorithms
Volume6
Issue number2-3
DOIs
Publication statusPublished - 1995

Fingerprint

Random Graphs
Labeling
Irregular
Edge Labeling
Vertex Degree
Graph in graph theory
Packing
Pairwise
Triangle
Assignment
Valid
Distinct
Estimate

ASJC Scopus subject areas

  • Software
  • Mathematics(all)
  • Computer Graphics and Computer-Aided Design
  • Applied Mathematics

Cite this

How to make a random graph irregular. / Tuza, Z.

In: Random Structures & Algorithms, Vol. 6, No. 2-3, 1995, p. 323-329.

Research output: Contribution to journalArticle

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