Skewness of graphs with small cutsets

The skewness of a graph is the minimum number of edges that have to be removed to leave a planar subgraph. This is complementary, and computationally equivalent, to the Maximum Planar Subgraph problem. In this paper we look at the problem of computing the skewness of a graph with a small cutset. We show how to express the skewness of a graph with a cutset of size at most 4 in terms of the skewnesses of several derived graphs obtained by cutting along that cutset and `stitching up' afterwards. We conclude with a discussion on possible applications to planarisation.