In an edge deletion problem one is asked to delete at most k edges from a given graph such that the resulting graph satisfies a certain property. In this work, we study four NP-complete edge deletion problems where the goal graph has to be a chain, a split, a threshold, or a co-trivially perfect graph, respectively. All these four graph classes are characterized by a common forbidden induced su...

We study the computational complexity of k-anonymizing a given graph by as few graph contractions as possible. A graph is said to be k-anonymous if for every vertex in it, there are at least k − 1 other vertices with exactly the same degree. The general degree anonymization problem is motivated by applications in privacy-preserving data publishing, and was studied to some extent for various gra...

The MaxSTC problem is an assignment of the edges with strong or weak labels having the maximum number of strong edges such that any two vertices that have a common neighbor with a strong edge are adjacent. The Cluster Deletion problem seeks for the minimum number of edge removals of a given graph such that the remaining graph is a disjoint union of cliques. Both problems are known to be NP-hard...

Cluster Editing is the problem of turning a graph into a cluster graph, that is, a disjoint union of cliques, by a minimum number of edge edits. Cluster Deletion is similarly defined, with edge deletions only. We propose a local notion of edit-optimality: Informally, we say that a crown (a certain type of labeled graph) is edit-optimal if it yields a cluster in some optimal solution to Cluster ...

an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

We look for graph polynomials which satisfy recurrence relations on three kinds of edge elimination: edge deletion, edge contraction and deletion of edges together with their end points. Like in the case of deletion and contraction only (W. Tutte, 1954), it turns out that there is a most general polynomial satisfying such recurrence relations, which we call ξ(G, x, y, z). We show that the new p...

Given a graph G and an integer k, the paw-free completion problem asks whether it is possible to add at most k edges make paw-free. The edge deletion defined analogously. Sandeep Sivadasan (IPEC 2015) asked these problems admit polynomial kernels. We answer both questions affirmatively by presenting, respectively, O(k)-vertex O(k4)-vertex kernels for them. This part of ongoing program that aims...

objective: interaction between genetic and environmental factors is considered as major factors in schizophrenia (scz). it has been shown that dopaminergic and noradrenergic neurotransmission dysfunction play an essential role in the scz pathogenesis. this study aimed to find the impact of functional 19-bp insertion/deletion (ins/del) polymorphism in dopamine beta-hydroxylase (dbh) gene on scz ...

Let G = ( U U V, E ) be a weighted bipartite graph having an edge weight u’, 2 0 for each e in E . An edge is called a must vitul edge if its removal from G results in the largest decrease in the total weight of the maximum weighted matching. In [I] , an O( n 3 ) algorithm was presented to obtain the most vital edges. In [ 3 ] , Volgenant pointed out that the most vital edges can also be found ...