Findings reveal approximate path decompositions in regular graphs, indicating a solution to Kotzig's problem and supporting previous conjectures.
We show that the edges of any ‐regular graph can be almost decomposed into paths of length roughly , giving an approximate solution to a problem of Kotzig from 1957. Along the way, we show that almost all of the vertices of a ‐regular graph can be partitioned into paths, asymptotically confirming a conjecture of Magnant and Martin from 2009.
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Montgomery et al. (2025) studied this question.
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