Abstract In 1958 L. Fejes Tóth and J. Molnar proposed a conjecture about a lower bound for the thinnest covering of the plane by circles with arbitrary radii from a given interval of the reals. If only two kinds of radii can occur this conjecture was in essence proven by A. Florian in 1962, leaving the general case unanswered till now. The goal of this paper is to analytically describe the general case in such a way that the conjecture can easily be numerically verified and upper and lower limits for the asserted bound can be gained.

中文翻译：

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具有非全等圆的欧几里得平面的最薄覆盖

摘要 1958 年，L. Fejes Tóth 和 J. Molnar 提出了一个关于平面最薄覆盖的下界的猜想，该下界由具有给定实数间隔的任意半径的圆构成。如果只有两种半径可以出现，这个猜想本质上已经被 A. Florian 在 1962 年证明了，直到现在一般情况都没有得到解答。本文的目标是以这样一种方式分析描述一般情况，即可以轻松地在数值上验证猜想，并且可以获得断言边界的上限和下限。