Packing and Covering Triangles in Bilaterally-Complete Tripartite Graphs
摘要
We use Menger’s Theorem and König’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.