Year: 2022
Type: preprint
Abstract: We show that there is a constant $C$ such that for every $\varepsilon>0$ any $2$-coloured $K_n$ with minimum degree at least $n/4+\varepsilon n$ in both colours contains a complete subgraph on $2t$ vertices where one colour class forms a $K_{t,t}$, provided that $n\geq \varepsilon^{-Ct}$. Also, we prove that if $K_n$ is $2$-coloured with minimum degree at least $\varepsilon n$ in both colours then it must contain one of two natural colourings of a complete graph. Both results are tight up to the value of $C$ and they answer two recent questions posed by Kamčev and Müyesser.
Source: arXiv (Cornell University)
Authors: Girão, António, Correia, David Munhá
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4308244649