… giving a new simple recognition algorithm for split graphs. We apply these results to the
following generalization of split graphs: A graph is said to be a (k, /)-graph if its vertex set can be …

… a minimal triangulation of the given graph. Generalized split graphs can be recognized via
this algorithm in O ( n 3 ) time. We give algorithms on unipolar graphs for finding a maximum …

… of graphs. In [EG] the minimum order of split critical graphs studied (under a more general …
This paper is focused on the maximum order of a (p, q)-split critical graph. It is not clear a priori …

… circular split systems introduced in [1]. In fact, any system of splits can be visualized by a
splits graph, … 1, we depict a splits graph representing a set of splits obtained by combining the …

… values of t over the class of such graphs G be denoted by Tk, z … Let M(n, k, l) be the generalized
graph of n vertices defined … We use induction on p. If p = 1 there can be only one pair of …

… If |X| ¡k then we include X into A0 (the set A0 depends on X). By Claim B, we may omit the …
Otherwise we include a transversal Y into A1 (the set A1 depends on X and Y). By Claim B, we …

… This chapter focuses on split graphs. An undirected … There is no restriction on edges between
vertices of S and vertices of K. In general, the partition V = S + K of a split graph will not be …

… We first update the equivalent graph EG for the split. To accomplish … a maximum flow
from r to s on the (changing… graph G. Let Pt be a path of flow from r to s ending in edge ts. …

… splitting functions for which the problem is NP-hard. Finally, we outline several open questions
on general … for our results on reducing hypergraph cut problems to graph cut problems. …

… In Table 1, we compare some values of the split factor s for q = 10−3, for which the graph
unreliability is approximately 2×10−9, and n = 107. When s increases, the number of levels …