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 n 1 , n 2 , and n 3 sufficiently large, we determine and exactly and within an additive constant. We also include general constructions of ‐saturated subgraphs of with few edges for .