Paintshop, odd cycles and necklace splitting
Discrete Applied Mathematics
Discrete Fixed Points: Models, Complexities, and Applications
Mathematics of Operations Research
Computing solutions of the paintshop-necklace problem
Computers and Operations Research
Algorithmic Solutions for Envy-Free Cake Cutting
Operations Research
Algorithmic Solutions for Envy-Free Cake Cutting
Operations Research
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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.