Divisible subdivisions
We prove that for every graph H of maximum degree at most 3 and for every positive integer q there is a finite f = f ( H , q ) such that every K f‐minor contains a subdivision of H in which every edge is replaced by a path whose length is divisible by q. For the case of cycles we show that for f = O...
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Veröffentlicht in: | Journal of graph theory 2021-12, Vol.98 (4), p.623-629 |
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Hauptverfasser: | , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
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Zusammenfassung: | We prove that for every graph
H of maximum degree at most 3 and for every positive integer
q there is a finite
f
=
f
(
H
,
q
) such that every
K
f‐minor contains a subdivision of
H in which every edge is replaced by a path whose length is divisible by
q. For the case of cycles we show that for
f
=
O
(
q
log
q
) every
K
f‐minor contains a cycle of length divisible by
q, and observe that this settles a recent problem of Friedman and the second author about cycles in (weakly) expanding graphs. |
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ISSN: | 0364-9024 1097-0118 |
DOI: | 10.1002/jgt.22716 |