Domination numbers and homotopy in certain ternary graphs
Combinatorics
2025-08-04 v1
Abstract
A ternary graph is a graph with no induced cycles of length modulo . It was recently shown that, if the independence complex of a ternary graph is not contractible, then it is homotopy equivalent to a sphere. When a ternary graph also does not contain induced cycles of length modulo , we prove that the dimension of the sphere is equal to the dimension of a minimum maximal simplex of the independence complex, or equivalently, to the value obtained by subtracting from the independent domination number of the graph. The same statement holds if we replace the independent domination number with the domination number. We also give a hypergraph analogue of the statement above.
Cite
@article{arxiv.2508.00699,
title = {Domination numbers and homotopy in certain ternary graphs},
author = {Taehyun Eom and Jinha Kim and Minki Kim},
journal= {arXiv preprint arXiv:2508.00699},
year = {2025}
}