PreprintCC BY 4.0arXiv
Forcing monochromatic subdivisions
Abstract
We prove that for every integers d ≥ 1 and s≥2 there exists an integer D, that depends only on d and s, such that for every graph P with maximum degree at most $ d$, there is a graph H with maximum degree at most D in which every s-coloring of V(H) yields a monochromatic subdivision of P.
Related
BibTeX
@misc{collado2026forcing,
title = {{Forcing monochromatic subdivisions}},
author = {Gabriel Collado and Dhruv Mubayi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.00636},
eprint = {2609.00636},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.00636},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Forcing monochromatic subdivisions
AU - Gabriel Collado
AU - Dhruv Mubayi
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.00636
UR - https://arxiv.org/abs/2609.00636
AB - We prove that for every integers d ≥ 1 and s≥2 there exists an integer D, that depends only on d and s, such that for every graph P with maximum degree at most $ d$, there is a graph H with maximum degree at most D in which every s-coloring of V(H) yields a monochromatic subdivision of P.
ER -