Saturation Numbers in Tripartite Graphs

Given graphs H and F, a subgraph is an F-saturated subgraph of H if , but for all . The saturation number of F in H, denoted , is the minimum number of edges in an F-saturated subgraph of H. In this article, we study saturation numbers of tripartite graphs in tripartite graphs. For and n1, n2, and n3 sufficiently large, we determine and exactly and within an additive constant. We also include general constructions of -saturated subgraphs of with few edges for .