The 1‐2‐3‐conjecture holds for dense graphs
Liang Zhong · Journal of Graph Theory · 2018
Abstract 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 such that every graph with and , where is the minimum degree of satisfying the 1‐2‐3‐conjecture.