Decomposition of bounded degree graphs into C4-free subgraphs
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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: edge-colouring, graph decomposition, graphs of bounded maximum degree, degree Ramsey numbers,bipartite Turán numbers. MSC: 05C15, 05D40, 05C35, 05C55.
CitationKang, R.; Perarnau-Llobet, G. Decomposition of bounded degree graphs into C4-free subgraphs. "European journal of combinatorics", 15 Octubre 2014, vol. 44, núm. Part A, p. 99-105.