Kernelization and Parameterized Algorithms for 3-Path Vertex Cover

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 whether a graph has a 3-path vertex cover of size at most $k$. In this paper, we give a kernel of $5k$ vertices and an $O^*(1.7485^k)$-time and polynomial-space algorithm for this problem, both new results improve previous known bounds.Comment: in TAMC 2016, LNCS 9796, 201

Connected-domination triangle graphs, perfect connected-neighbourhood graphs and connected neighbourhood sets

We introduce and characterize the class of graphs in which every connected dominating set is a (connected) neighbourhood set and the class of graphs whose all connected induced subgraphs have equal minimum neighbourhood set and minimum connected neighbourhood set cardinalities. Assuming P - NP, we also prove that the minimum connected neighbourhood set problem cannot be approximated within a logarithmic factor in polynomial time in their common subclass, the class of simplicial split graphs

Approximability for the minimum and maximum induced matching problems

International audienc

Approximability for the minimum and maximum induced matching problems

International audienc