Rainbow spanning configurations in uniformly coloured pseudorandom graphs

@misc{aignerhorev2026rainbow,
  title = {{Rainbow spanning configurations in uniformly coloured pseudorandom graphs}},
  author = {Elad Aigner-Horev and Dan Hefetz and Yury Person and Michael Trushkin},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.26329},
  eprint = {2609.26329},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.26329},
}

TY  - UNPB
TI  - Rainbow spanning configurations in uniformly coloured pseudorandom graphs
AU  - Elad Aigner-Horev
AU  - Dan Hefetz
AU  - Yury Person
AU  - Michael Trushkin
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.26329
UR  - https://arxiv.org/abs/2609.26329
AB  - We prove a quantitative palette-transference principle for rainbow spanning configurations in uniformly edge-coloured pseudorandom graphs. The input to our transference principle is an embedding result of a spanning configuration in an appropriately bijumbled graph H with sufficiently large minimum degree. The output of our transference principle is the asymptotically almost sure existence of a rainbow copy of the same configuration in a uniformly edge-coloured graph G whose bijumbledness and minimum are comparable and sometimes coincide with those of H. We then apply our transference principle in order to asymptotically almost surely obtain K_k-factors, including perfect matchings, Hamilton cycles, and a prescribed bounded-degree spanning tree in bijumbled graphs with appropriate parameters. In all of our results, the palette size exceeds the size of the target configuration by ε n, where ε > 0 is arbitrarily small yet fixed, and n is the order of the configuration.
ER  -