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arXiv · 1701.06705

Generalized Gray codes with prescribed ends of small dimensions

Tomáš Dvořák·Václav Koubek
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Abstract

Given pairwise distinct vertices $\{α_i , β_i\}^k_{i=1}$ of the $n$-dimensional hypercube $Q_n$ such that the distance of $α_i$ and $β_i$ is odd, are there paths $P_i$ between $α_i$ and $β_i$ such that $\{V (P_i)\}^k_{i=1}$ partitions $V(Q_n)$? A positive solution for every $n\ge1$ and $k=1$ is known as a Gray code of dimension $n$. In this paper we settle this problem for small values of $n$.

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Tomáš Dvořák, Václav Koubek. 2017-01-24. Generalized Gray codes with prescribed ends of small dimensions. https://arxiv.org/abs/1701.06705

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