Given a forest F = (V, E) and a positive integer D, we consider the problem of finding a minimum number of new edges E such that in the augmented graph H = (V, E∪E ) any pair of...
Many parameterized algorithms for NP-hard graph problems are search tree algorithms with sophisticated local branching rules. But it has also been noticed that the global structur...
In this work we introduce the class of graphs with bounded induced distance of order k, (BID(k) for short). A graph G belongs to BID(k) if the distance between any two nodes in ev...
For a connected graph G, let L(G) denote the maximum number of leaves in a spanning tree in G. The problem of computing L(G) is known to be NP-hard even for cubic graphs. We improv...
We give an O(n log n) algorithm for computing the girth (shortest cycle) of an undirected n-vertex planar graph. Our solution extends to any graph of bounded genus. This improves u...