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Decomposition of bounded degree graphs into C4-free subgraphs

We prove that every graph with maximum degree ∆ admits a partition of its edges into O(√∆) parts (as ∆→∞) none of which contains C4 as a subgraph. This bound is sharp up to a constantfactor. Our proof uses an iterated random colouring procedure.Keywords:
Kang, Ross, Perarnau Llobet, Guillem
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