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  • Parameterized Complexity of Satisfactory Partition Problem 
    GAIKWAD, AJINKYA; MAITY, SOUMEN; TRIPATHI, SHUVAM KANT (Springer Nature, 2020-12)
    The Satisfactory Partition problem consists in deciding if the set of vertices of a given undirected graph can be partitioned into two nonempty parts such that each vertex has at least as many neighbours in its part as in ...
  • Parameterized Complexity of Locally Minimal Defensive Alliances 
    GAIKWAD, AJINKYA; MAITY, SOUMEN; TRIPATHI, SHUVAM KANT (Springer Nature, 2021-01)
    A defensive alliance in a graph G=(V,E) is a set of vertices S satisfying the condition that every vertex v∈S has at least as many neighbours (including itself) in S as it has in V∖S . We consider the notion of local ...
  • Parameterized Complexity of Defensive and Offensive Alliances in Graphs 
    GAIKWAD, AJINKYA; MAITY, SOUMEN; TRIPATHI, SHUVAM KANT (Springer Nature, 2021-01)
    In this paper we study the problem of finding small defensive and offensive alliances in a simple graph. Given a graph G=(V,E) and a subset S⊆V(G) , we denote by dS(v) the degree of a vertex v∈V in G[S], the subgraph of G ...
  • The Balanced Satisfactory Partition Problem 
    GAIKWAD, AJINKYA; MAITY, SOUMEN; TRIPATHI, SHUVAM KANT (Springer Nature, 2021-01)
    The Satisfactory Partition problem asks whether it is possible to partition the vertex set of a given undirected graph into two parts such that each vertex has at least as many neighbours in its own part as in the other ...
  • Parameterized Intractability of Defensive Alliance Problem 
    GAIKWAD, AJINKYA; MAITY, SOUMEN; TRIPATHI, SHUVAM KANT (Springer Nature, 2022-01)
    The DEFENSIVE ALLIANCE problem has been studied extensively during the last twenty years. A set R of vertices of a graph is a defensive alliance if, for each element of R, the majority of its neighbours are in R. The problem ...

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