We study the parameterized complexity of the following problem: is it possible to make a given graph r-regular by applying at most k elementary editing operations; the operations are vertex deletion, edge deletion, and edge addition. We also consider more general annotated variants of this problem, where vertices and edges are assigned an integer cost and each vertex v has assigned its own desi...

We study the complexity of graph modification problems with respect to homomorphism-based colouring properties edge-coloured graphs. A homomorphism from $G$ $H$ is a vertex-mapping that preserves adjacencies and edge-colours. consider property having fixed $H$. The question we are interested in is: given an $G$, can perform $k$ operations so resulting admits $H$? vertex-deletion, edge-deletion ...

For a graph H, the H-free Edge Deletion problem asks whether there exist at most k edges whose deletion from the input graph G results in a graph without any induced copy of H. H-free Edge Completion and H-free Edge Editing are defined similarly where only completion (addition) of edges are allowed in the former and both completion and deletion are allowed in the latter. We completely settle th...

We propose a new random graph model—Edge Popularity—for the web graph and other complex networks, where edges are deleted over time and an edge is chosen to be deleted with probability inversely proportional to the in-degree of the destination. We show that with probability tending to one as time tends to infinity, the model generates graphs whose degree distribution follows a power law. Depend...

We study the computational complexity of $c$-Colored $P_\ell$ Deletion and $C_\ell$ Deletion. In these problems, one is given a $c$-edge-colored graph wants to destroy all induced $c$-colored paths or cycles, respectively, on $\ell$ vertices by deleting at most $k$ edges. Herein, path cycle if it contains edges $c$ distinct colors. show that are NP-hard for each non-trivial combination $\ell$. ...

Streaming is a model where an input graph provided one edge at time, instead of being able to inspect it will. In this work, we take parameterized approach by assuming vertex cover the given, building on work Bishnu et al. [COCOON 2020]. We show further potency combining parameter with Adjacency List streaming obtain results for deletion problems. This includes kernels, algorithms, and lower bo...

A recent formalization of Iterative Belief Propagation (IBP) has shown that it can be understood as an exact inference algorithm on an approximate model that results from deleting every model edge. This formalization has led to (1) new realizations of Generalized Belief Propagation (GBP) in which edges are recovered incrementally to improve approximation quality, and (2) edgerecovery heuristics...

For a graph H, the H-free Edge Deletion problem asks whether there exist at most k edges whose deletion from the input graph G results in a graph without any induced copy of H. We prove that H-free Edge Deletion is NP-complete if H is a graph with at least two edges and H has a component with maximum number of vertices which is a tree or a regular graph. Furthermore, we obtain that these NP-com...

A well-known problem in data science and machine learning is linear regression, which recently extended to dynamic graphs. Existing exact algorithms for updating the solution of graph regression require at least a time (in terms n: size graph). However, this complexity might be intractable practice. In current paper, we utilize subsampled randomized Hadamard transformand CountSketchto propose f...

In the {Claw, Diamond}-Free Edge Deletion problem, we are given a graph G and an integer k > 0, the question is whether there are at most k edges whose deletion results in a graph without claws and diamonds as induced graphs. Based on some refined observations, we propose a kernel of O(k3) vertices and O(k4) edges, significantly improving the previous kernel of O(k12) vertices and O(k24) edges....