New Bounds for the Snake-in-the-Box Problem
Abstract
The Snake-in-the-Box problem is that of finding a longest induced path in an $n$-dimensional hypercube. We prove new lower bounds for the values $n\in \{11,12,13\}$. The Coil-in-the-Box problem is that of finding a longest induced cycle in an $n$-dimensional hypercube. We prove new lower bounds for the values $n\in \{12,13\}$.
- Publication:
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arXiv e-prints
- Pub Date:
- March 2016
- DOI:
- 10.48550/arXiv.1603.05119
- arXiv:
- arXiv:1603.05119
- Bibcode:
- 2016arXiv160305119A
- Keywords:
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- Mathematics - Combinatorics;
- Computer Science - Discrete Mathematics
- E-Print:
- We improved six lower bounds from the previous version (two for snake-in-the-box and four for coil-in-the-box)