1,2,3-Conjecture and 1,2-Conjecture for Sparse Graphs

Abstract

We apply the Discharging Method to prove the 1,2,3-Conjecture and the 1,2-Conjecture for graphs with maximum average degree less than 8/3. Stronger results on these conjectures have been proved, but this is the first application of discharging to them, and the structure theorems and reducibility results are of independent interest.

29 pages, 19 figures; same results as earlier version, but revised introduction