The partite saturation number of spider

摘要

Let H[n] denote the blow-up of H onto parts of size n. A copy of H in H[n] is partite if it has one vertex in each part of H[n]. It is an interesting question that how few edges a subgraph G of H[n] can have such that G has no partite copy of H but the addition of any new edge from H[n] creates a partite H. A spider graph is a tree having at most one vertex with degree greater than two. This paper considers the partite saturation number of spiders, which can be seen as an extension of the results for stars and paths in [22].