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A new lower bound for the multicolor Ramsey number $r k(K {2, t + 1})$ by Taranchuk, Vladislav is a scholarly article available to read on EtoBox.

What is A new lower bound for the multicolor Ramsey number $r k(K {2, t + 1})$ about?

In this short note, we provide a new infinite family of $K_{2, t+1}$-free graphs for each prime power $t$. Using these graphs, we show that it is possible to partition the edges of $K_n$ into parts, such that each part is isomorphic to our $K_{2, t+1}$-free graph. This yields an improved lower bound to the multicolor Ramsey number $r_k(K_{2, t+1})$ when $k$ and $t$ are powers of the same prime. For these values of $k$ and $t$, our coloring implies that $$ tk^2 + 1 \leq r_k(K_{2, t+1}) \leq tk^2 + k + 2. $$ where the upper bound is due to Chung and Graham.

Author

Taranchuk, Vladislav

Published

2024

Language

EN