Minimum k-path vertex cover

Authors:
Boštjan Brešar;František Kardoš;Ján Katrenič;Gabriel Semanišin
Affiliations:
Faculty of Natural Science and Mathematics, University of Maribor, Slovenia and Institute of Mathematics, Physics and Mechanics, Ljubljana, Slovenia;Institute of Mathematics, P.J. Šafárik University, Košice, Slovakia;Institute of Computer Science, P.J. Šafárik University, Košice, Slovakia;Institute of Computer Science, P.J. Šafárik University, Košice, Slovakia
Venue:
Discrete Applied Mathematics
Year:
2011

Citing 11
Cited 5

Generalized colorings of graphs

Graph theory with applications to algorithms and computer science
Introduction to algorithms

Introduction to algorithms
The monadic second-order logic of graphs. I. recognizable sets of finite graphs

Information and Computation
On the independence number of a graph in terms or order and size

Discrete Mathematics
A new proof of the independence ratio of triangle-free cubic graphs

Discrete Mathematics
Coloring with Defects

Coloring with Defects
Total domination of graphs and small transversals of hypergraphs

Combinatorica
Finding paths of length k in O∗(2k) time

Information Processing Letters
Independence, odd girth, and average degree

Journal of Graph Theory
Protocol analysis for concrete environments

EUROCAST'05 Proceedings of the 10th international conference on Computer Aided Systems Theory
Design and analysis of a generalized canvas protocol

WISTP'10 Proceedings of the 4th IFIP WG 11.2 international conference on Information Security Theory and Practices: security and Privacy of Pervasive Systems and Smart Devices

On computing the minimum 3-path vertex cover and dissociation number of graphs

Theoretical Computer Science
A primal-dual approximation algorithm for the vertex cover P3 problem

Theoretical Computer Science
K-reach: who is in your small world

Proceedings of the VLDB Endowment
The vertex cover P3 problem in cubic graphs

Information Processing Letters
On the vertex k-path cover

Discrete Applied Mathematics

Quantified Score

Hi-index	0.05

Visualization

Abstract

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. Denote by @j"k(G) the minimum cardinality of a k-path vertex cover in G. It is shown that the problem of determining @j"k(G) is NP-hard for each k=2, while for trees the problem can be solved in linear time. We investigate upper bounds on the value of @j"k(G) and provide several estimations and exact values of @j"k(G). We also prove that @j"3(G)@?(2n+m)/6, for every graph G with n vertices and m edges.