A Solution to the 1-2-3 Conjecture
arXiv:2303.02611 · doi:10.1016/j.jctb.2024.01.002
Abstract
We show that for every graph without isolated edge, the edges can be assigned weights from {1,2,3} so that no two neighbors receive the same sum of incident edge weights. This solves a conjecture of Karoński, Luczak, and Thomason from 2004.
16 pages