**Beiträge zur Algebra und Geometrie / Contributions to Algebra and GeometryVol. 40, No. 1, pp. 217-227 (1999)
**

#
What is the Minimum Length of a

Non-Extendable Lace?

##
Arnfried Kemnitz, Valeriu Soltan

Abt. Diskrete Mathematik, Techn. Universität Braunschweig, D-38106 Braunschweig, Germany
Mathematical Institute, Academy of Sciences of Moldova, MD-2028 Chisinau, Moldova

**Abstract:** A family $\{C_1,...,C_n\}$ of pairwise distinct, non-overlapping, congruent circles in the plane form a * lace* provided $C_i$ touches $C_{i+1}$ for all $i = 1,\ldots,n-1$. If, additionally, $C_n$ touches $C_1$, the lace is named a * loop*. A lace (loop) $\{C_1,\ldots, C_n\}$ is called * extendable* if it is properly contained in another lace (respectively, loop). In the paper various problems and results on minimum lengths of non-extendable laces and loops are discussed.

**Keywords:** finite packing, circles, plane

**Classification (MSC91):** 52C15

**Full text of the article:**

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