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The 1‐2‐3‐conjecture holds for dense graphs
Author(s) -
Zhong Liang
Publication year - 2019
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.22413
Subject(s) - conjecture , mathematics , combinatorics , graph , order (exchange) , lonely runner conjecture , enhanced data rates for gsm evolution , degree (music) , collatz conjecture , discrete mathematics , computer science , telecommunications , physics , finance , acoustics , economics
This paper confirms the 1‐2‐3‐conjecture for graphs that can be edge‐decomposed into cliques of order at least 3. Furthermore we combine this with a result by Barber, Kühn, Lo, and Osthus to show that there is a constants n ′ > 0 such that every graph G with ∣ V ( G ) ∣ ≥ n ′ and δ ( G ) > 0.99985 ∣ V ( G ) ∣ , where δ ( G ) is the minimum degree of G satisfying the 1‐2‐3‐conjecture.