English

Not all partial cubes are $\Theta$-graceful

Combinatorics 2020-01-07 v2

Abstract

It is shown that the graph obtained by merging two vertices of two 4-cycles is not a Θ\Theta-graceful partial cube, thus answering in the negative a question by Bre\v{s}ar and Klav\v{z}ar from [1], who asked whether every partial cube is Θ\Theta-graceful.

Cite

@article{arxiv.1809.05320,
  title  = {Not all partial cubes are $\Theta$-graceful},
  author = {Nathann Cohen and Matjaž Kovše},
  journal= {arXiv preprint arXiv:1809.05320},
  year   = {2020}
}
R2 v1 2026-06-23T04:06:22.444Z