Approximate path decompositions of regular graphs

Alp Muyesser, UCL
Fine Hall 224

We show that 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 vertices of a d-regular graph can be partitioned into n/(d+1) paths, asymptotically confirming a conjecture of Magnant and Martin from 2009. This is joint work with Richard Montgomery, Alexey Pokrovskiy, and Benny Sudakov.