1,2,3-Conjecture and 1,2-Conjecture for Sparse Graphs
classification
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conjecturedischarginggraphsresultsapplicationapplyaveragebeen
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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.
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