Let T be a tree with n nodes from which edges are deleted interspersed with m on-line connectivity queries. Even and Shiloach gave an O(n log n + m) algorithm to process edge deletion and m queries (An On-Line Edge-Deletion problem, J. ACM, Vol. 28, Nr. 1, 1981). In this paper we present an O(n + m) algorithm for the same problem.

Abstract The eccentricity matrix ? ( G ) of a graph is obtained from the distance by retaining largest distances in each row and column, leaving zeros remaining ones. energy sum absolute values eigenvalues ). Although matrices graphs are closely related to graphs, number properties substantially different those matrices. change due an edge deletion one such property. In this article, we give ex...

A diamond is a graph obtained by removing an edge from a complete graph on four vertices. A graph is diamond-free if it does not contain an induced diamond. The Diamond-free Edge Deletion problem asks to find whether there exist at most k edges in the input graph whose deletion results in a diamond-free graph. The problem was proved to be NP-complete and a polynomial kernel of O(k4) vertices wa...

Edge deletion problems ask for a minimum set of edges whose deletion makes a graph have a certain property. When this property can be characterized by a finite set of forbidden induced subgraphs, the problem can be solved in fixed-parameter time by a naive bounded search tree algorithm. Sometimes deleting an edge to break an erstwhile forbidden induced subgraph might introduce new ones, which m...

This paper studies algorithmic strategies to effectively reduce the number of infections in susceptible-infected-recovered (SIR) epidemic models. We consider a Markov chain SIR model and its two instantiations deterministic (D-SIR) independent cascade (IC-SIR) model. investigate problem minimizing by restricting contacts under realistic constraints. Under moderate assumptions on reproduction nu...

Many fixed-parameter tractable algorithms using a bounded search tree have been repeatedly improved, often by describing a larger number of branching rules involving an increasingly complex case analysis. We introduce a novel and general search strategy that branches on the forbidden subgraphs of a graph class relaxation. By using the class of P4-sparse graphs as the relaxed graph class, we obt...