Packing and Covering Triangles in Bilaterally-Complete Tripartite Graphs
Naivedya Amarnani, Amaury De Burgos, Wayne Broughton
TL;DR
This paper generalizes a known result about triangle packing and covering in complete tripartite graphs to a broader class of tripartite graphs with two complete sides, using classical graph theorems.
Contribution
It extends the triangle packing and covering equality to bilaterally-complete tripartite graphs, broadening the scope of previous results.
Findings
Maximum number of edge-disjoint triangles equals minimum edge cover in the specified graphs.
Utilizes Menger's Theorem and K"onig's Line Colouring Theorem for the proof.
Generalizes known results from complete tripartite graphs to bilaterally-complete tripartite graphs.
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.
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Taxonomy
TopicsAdvanced Graph Theory Research · graph theory and CDMA systems · Optimization and Packing Problems