Polynomial algorithms for computing the isolated toughness of interval and split graphs

The isolated toughness (Figure presented.) of a noncomplete graph G is defined as: (Figure presented.), where C(G) is the collection of all vertex cutsets of G and i(G − Y) stands for the number of isolated vertices in G − Y. If G is a complete graph, we set (Figure presented.). This isolated toughness parameter is closely related to the existence of factors and fractional factors in graphs. These factors and fractional factors are well-studied within graph theory, and have various applications in several fields related to computer science. In this article, we pay our attention to the computational complexity of computing the isolated toughness. We present polynomial algorithms for computing the exact value of (Figure presented.) for interval graphs and for split graphs, two well-studied special graph classes.