A new upper bound for mutually touching infinite cylinders

Abstract

Let $N$ denote the maximum number of congruent infinite cylinders that can be arranged in $\mathbb{R}^3$ so that every pair of cylinders touches each other. Littlewood posed the question of whether $N=7$, which remains unsolved. In this paper, we prove that $N\leq 18$, improving the previously known upper bound of $24$ established by A. Bezdek.