Rainbow clique subdivisions

We show that for any integer t >= 2, every properly edge colored n-vertex graph with average degree at least (log n)2+o(1) contains a rainbow subdivision of a complete graph of size t. Note this bound is within (log n)1+o(1) factor of the lower bound. This also implies a result on the rainbow Turan number of cycles.(c) 2023 Elsevier Ltd. All rights reserved.

Automated summary

We prove that for any integer t >= 2, every properly edge colored n-vertex graph with average degree at least (log n)2+o(1) contains a rainbow subdivision of a complete graph of size t. This result is within a (log n)1+o(1) factor of the lower bound, and also implies a result on the rainbow Turan number of cycles.