We study a family of closely-related distributed graph problems, which we call degree splitting, where roughly speaking the objective is to partition (or orient) the edges such that each node's degree is split almost uniformly. Our findings lead to answers for a number of problems, a sampling of which includes: -- We present a $poly(\log n)$ round deterministic algorithm for $(2\Delta-1)\cdot (1+o(1))$-edge-coloring, where $\Delta$ denotes the maximum degree... (read more)

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