As a well-known NP-hard problem, the vertex cover problem has broad applications, which
has aroused the concern of many researchers. In recent years, its related optimization …

Given a graph G=(V, E) and an integer k∊ ℕ, we study k-Vertex Separator (resp. k-Edge
Separator), where the goal is to remove the minimum number of vertices (resp. edges) such …

A dissociation set in a graph G=(V, E) is a vertex subset D such that the subgraph G [D]
induced on D has vertex degree at most 1. A 3-path vertex cover in a graph is a vertex …

A subset F of vertices of a graph G is called a vertex cover P t set if every path of order t in G
contains at least one vertex from F. Denote by ψ t (G) the minimum cardinality of a vertex …

Let P ℓ denote a path in a graph G=(V, E) with ℓ vertices. A vertex cover P ℓ set C in G is a
vertex subset such that every P ℓ in G has at least a vertex in C. The Vertex Cover P ℓ …

A 3-path vertex cover in a graph is a vertex subset C such that every path of three vertices
contains at least one vertex from C. The parameterized 3-path vertex cover problem asks …

A subset S of vertices of a graph G is called a k-path vertex cover if every path of order k in G
contains at least one vertex from S. The cardinality of a minimum k-path vertex cover is …

A subset F of vertices of a graph G is called a vertex cover Pk set if every path of order k in G
contains at least one vertex from F. Denote by ψk (G) the minimum cardinality of a vertex …

The general $ d $-position number ${\rm gp} _d (G) $ of a graph $ G $ is the cardinality of a
largest set $ S $ for which no three distinct vertices from $ S $ lie on a common geodesic of …

The dissociation number diss (G) diss(G) of a graph GG is the maximum order of a set of
vertices of GG inducing a subgraph that is of maximum degree at most 1. Computing the …