Packing and Covering Triangles in Bilaterally-Complete Tripartite Graphs
Combinatorics
2023-07-19 v1
Abstract
We use Menger's Theorem and K\"onig's Line Colouring Theorem to show that in any tripartite graph with two complete (bipartite) sides the maximum number of pairwise edge-disjoint triangles equals the minimum number of edges that meet all triangles. This generalizes the corresponding result for complete tripartite graphs given by Lakshmanan, et al.
Cite
@article{arxiv.2307.08824,
title = {Packing and Covering Triangles in Bilaterally-Complete Tripartite Graphs},
author = {Naivedya Amarnani and Amaury De Burgos and Wayne Broughton},
journal= {arXiv preprint arXiv:2307.08824},
year = {2023}
}
Comments
8 pages, 4 figures