We show that Meyniel weakly triangulated graphs are co-perfectly orderable (equivalently , that P 5-free weakly triangulated graphs are perfectly orderable). Our proof is algorithmic, and relies on a notion concerning separating sets, a property of weakly triangulated graphs, and several properties of Meyniel weakly triangulated graphs.
We use the notion of handle, introduced by Hayward, to improve algorithms for weakly chordal graphs. For recognition we reduce the time complexity from O(n2m) to O(rn 2) and the space complexity from O(n 3) to O(n + m), and also produce a hole or antihole if the input graph is not weakly chordal. For the optimization problems clique, independent set,… (More)
Let Q n be the random number of comparisons made by quicksort in sorting n distinct keys, when we assume that all n! possible orderings are equally likely. Known results concerning moments for Q n do not show how rare it is for Q n to make large deviations from its mean. Here we give a good approximation to the probability of such a large deviation, and… (More)
Many tasks require evaluating a specified Boolean expression ϕ over a set of probabilistic tests whose costs and success probabilities are each known. A strategy specifies when to perform which test, towards determining the overall outcome of ϕ. We are interested in finding the strategy with the minimum expected cost. As this task is typically NP-hard — for… (More)
Many tasks require evaluating a specified boolean expression φ over a set of probabilistic tests where we know the probability that each test will succeed, and also the cost of performing each test. A strategy specifies when to perform which test, towards determining the overall outcome of φ. This paper investigates the challenge of finding the… (More)
We establish results on NeST graphs (intersection tolerance graphs of neighborhood sub-trees of a tree) and several subclasses. In particular, we show the equivalence of proper NeST graphs and unit NeST graphs, the equivalence of ÿxed distance NeST graphs and threshold tolerance graphs, and the proper containment of NeST graphs in weakly chordal graphs. The… (More)