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We show that the edges of any d-regular graph can be almost decomposed into paths of length roughly d, giving an approximate solution to a problem of Kotzig from 1957. Along the way, we show that almost all of the vertices of a d-regular graph can be partitioned into n/ (d+1) paths, asymptotically confirming a conjecture of Magnant and Martin from 2009.
Montgomery et al. (Tue,) studied this question.
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