Abstract
An even cycle decomposition of a graph is a partition of its edges into even cycles. Markström constructed infinitely many 2-connected 4-regular graphs without even cycle decompositions. Máčajová and Mazák then constructed an infinite family of 3-connected 4-regular graphs without even cycle decompositions. In this note, we further show that there exists an infinite family of 4-connected 4-regular graphs without even cycle decompositions.
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