| Article ID: | iaor200954180 |
| Country: | United States |
| Volume: | 33 |
| Issue: | 3 |
| Start Page Number: | 678 |
| End Page Number: | 688 |
| Publication Date: | Aug 2008 |
| Journal: | Mathematics of Operations Research |
| Authors: | Meunier Frdric |
| Keywords: | necklace theorem |
This paper deals with direct proofs and combinatorial proofs of the famous necklace theorem of Alon, Goldberg, and West. The new results are a direct proof for the case of two thieves and three types of beads, and an efficient constructive proof for the general case with two thieves. This last proof uses a theorem of Ky Fan which is a version of Tucker's lemma concerning cubical complexes instead of simplicial complexes.