### Abstract

An irregular edge labeling of a graph G = (V, E) is a weight assignment f: E→ N such that the sums f ^{+} (v):= Σ_{v∈e∈E} f(e) are pairwise distinct. If such labelings exist in G, then the value of min_{f} Σ_{e∈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 n^{2}/4 + o(n^{2}) as n→∞, whenever p(n)‐n^{2/3}→∞. 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 language | English |
---|---|

Pages (from-to) | 323-329 |

Number of pages | 7 |

Journal | Random Structures & Algorithms |

Volume | 6 |

Issue number | 2-3 |

DOIs | |

Publication status | Published - 1995 |

### Fingerprint

### ASJC Scopus subject areas

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

### Cite this

*Random Structures & Algorithms*,

*6*(2-3), 323-329. https://doi.org/10.1002/rsa.3240060219

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

Research output: Contribution to journal › Article

*Random Structures & Algorithms*, vol. 6, no. 2-3, pp. 323-329. https://doi.org/10.1002/rsa.3240060219

}

TY - JOUR

T1 - How to make a random graph irregular

AU - Tuza, Z.

PY - 1995

Y1 - 1995

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84990686869&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990686869&partnerID=8YFLogxK

U2 - 10.1002/rsa.3240060219

DO - 10.1002/rsa.3240060219

M3 - Article

AN - SCOPUS:84990686869

VL - 6

SP - 323

EP - 329

JO - Random Structures and Algorithms

JF - Random Structures and Algorithms

SN - 1042-9832

IS - 2-3

ER -