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In this paper, we solve the maximum agreement sub-tree problem for a set T of k rooted, leaf-labelled evolutionary trees on n leaves where T contains a binary tree. We show that the O(kn 3)-time dynamic programming algorithm proposed by Farach et al. [10] and Bryant [7] can be implemented in O(n 2 log k−1 n) and O(k · n 3− 1 k−1) using the k-dimensional… (More)

A set S of vertices in a digraph D = (V, A) is a kernel if S is independent and every vertex in V − S has an out-neighbor in S. We show that there exist O(n2 19.1 √ k + n 4)-time and O(2 19.1 √ k k 9 + n 2)-time algorithms for checking whether a planar digraph D of order n has a kernel with at most k vertices. Moreover, if D has a kernel of size at most k,… (More)

In this paper we study the edge-thickness and the clique-thickness of a graph. The edge-thickness of a graph is defined as the thickness of the family of edges. The clique-thickness of a graph is defined as the thickness of the family of maximal cliques. Edges and maximal cliques of a graph are both considered as a collection of subsets of the vertex set.… (More)