@article{6b006676e5294f7cb4720705d6c5fa76,
title = "Divisible subdivisions",
abstract = "We prove that for every graph (Formula presented.) of maximum degree at most 3 and for every positive integer (Formula presented.) there is a finite (Formula presented.) such that every (Formula presented.) -minor contains a subdivision of (Formula presented.) in which every edge is replaced by a path whose length is divisible by (Formula presented.). For the case of cycles we show that for (Formula presented.) every (Formula presented.) -minor contains a cycle of length divisible by (Formula presented.), and observe that this settles a recent problem of Friedman and the second author about cycles in (weakly) expanding graphs.",
keywords = "complete minors, cycles, divisibility, expanders, subdivisions",
author = "Noga Alon and Michael Krivelevich",
note = "Publisher Copyright: {\textcopyright} 2021 Wiley Periodicals LLC",
year = "2021",
doi = "10.1002/jgt.22716",
language = "אנגלית",
volume = "98",
pages = "623--629",
journal = "Journal of Graph Theory",
issn = "0364-9024",
publisher = "Wiley-Liss Inc.",
number = "4",
}