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}
}
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4 pages