English

A counterexample to a conjecture of Ghosh

Combinatorics 2014-12-23 v1

Abstract

We answer two questions of Shamik Ghosh in the negative. We show that there exists a lobster tree of diameter less than 6 which accepts no alpha-labeling with two central vertices labeled by the critical number and the maximum vertex label. We also show a simple example of a tree of diameter 4, with an even degree central vertex which does not accept a maximum label in any graceful labeling.

Cite

@article{arxiv.1412.6984,
  title  = {A counterexample to a conjecture of Ghosh},
  author = {Hung Hua and Elliot Krop and Christopher Raridan},
  journal= {arXiv preprint arXiv:1412.6984},
  year   = {2014}
}

Comments

4 pages

R2 v1 2026-06-22T07:40:39.584Z