Korándi, D;
Lang, R;
Letzter, S;
Pokrovskiy, A;
(2021)
Minimum degree conditions for monochromatic cycle partitioning.
Journal of Combinatorial Theory, Series B
, 146
pp. 96-123.
10.1016/j.jctb.2020.07.005.
Preview |
Text
r-colours-final.pdf - Accepted Version Download (418kB) | Preview |
Abstract
A classical result of Erd˝os, Gy´arf´as and Pyber states that any r-edge-coloured complete graph has a partition into O(r 2 log r) monochromatic cycles. Here we determine the minimum degree threshold for this property. More precisely, we show that there exists a constant c such that any r-edge-coloured graph on n vertices with minimum degree at least n/2 + c · r log n has a partition into O(r 2 ) monochromatic cycles. We also provide constructions showing that the minimum degree condition and the number of cycles are essentially tight.
| Type: | Article |
|---|---|
| Title: | Minimum degree conditions for monochromatic cycle partitioning |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1016/j.jctb.2020.07.005 |
| Publisher version: | https://doi.org/10.1016/j.jctb.2020.07.005 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Monochromatic cycle partitioning, Ramsey theory, Hamilton cycles, Dirac-type problems |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10107291 |
Archive Staff Only
 |
View Item |
