Divisible subdivisions

Abstract We prove that for every graph of maximum degree at most 3 and for every positive integer there is a finite such that every ‐minor contains a subdivision of in which every edge is replaced by a path whose length is divisible by . For the case of cycles we show that for every ‐minor contains a cycle of length divisible by , and observe that this settles a recent problem of Friedman and the second author about cycles in (weakly) expanding graphs.