Generalized Gray codes with prescribed ends of small dimensions
Tom\'a\v{s} Dvo\v{r}\'ak, V\'aclav Koubek

TL;DR
This paper investigates the existence of specific path partitions in hypercubes with prescribed endpoints, providing solutions for small dimensions, advancing the understanding of Gray codes with particular boundary conditions.
Contribution
The paper solves the problem of partitioning hypercube vertices into paths with prescribed odd-distance endpoints for small dimensions, extending known results for Gray codes.
Findings
Established existence of such path partitions for small n
Extended Gray code constructions to new boundary conditions
Provided constructive methods for small hypercube dimensions
Abstract
Given pairwise distinct vertices of the -dimensional hypercube such that the distance of and is odd, are there paths between and such that partitions ? A positive solution for every and is known as a Gray code of dimension . In this paper we settle this problem for small values of .
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Taxonomy
TopicsLimits and Structures in Graph Theory · Finite Group Theory Research · Graph theory and applications
