Discrete Applied Mathematics, ISSN 0166-218X, 05/2016, Volume 205, pp. 101 - 108

A vertex subset C of a connected graph G is called a connected k-path vertex cover (CVCPk) if every path on k vertices contains at least one vertex from C, and...

Tree | Connected [formula omitted]-path vertex cover | Approximation algorithm | Girth | Weight | Connected k-path vertex cover | Algorithms

Tree | Connected [formula omitted]-path vertex cover | Approximation algorithm | Girth | Weight | Connected k-path vertex cover | Algorithms

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 09/2013, Volume 161, Issue 13-14, pp. 1943 - 1949

A subset S of vertices of a graph G is called a vertex k-path cover if every path of order k in G contains at least one vertex from S. Denote by ψk(G) the...

Regular graphs | Grids | Average degree | [formula omitted]-path vertex cover | k-path vertex cover | MATHEMATICS, APPLIED | BIPARTITE GRAPHS

Regular graphs | Grids | Average degree | [formula omitted]-path vertex cover | k-path vertex cover | MATHEMATICS, APPLIED | BIPARTITE GRAPHS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 04/2019, Volume 347, pp. 723 - 733

A k-path vertex cover (VCPk) is a vertex set C of graph G such that every path of G on k vertices has at least one vertex in C. Because of its background in...

Approximation algorithm | Non-submodular potential function | Weight | Connected k-path vertex cover | MATHEMATICS, APPLIED | SET | P-3 PROBLEM

Approximation algorithm | Non-submodular potential function | Weight | Connected k-path vertex cover | MATHEMATICS, APPLIED | SET | P-3 PROBLEM

Journal Article

Discrete Mathematics, ISSN 0012-365X, 01/2013, Volume 313, Issue 1, pp. 94 - 100

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 ψk(G) the...

Vertex cover | Dissociation number | Independence number | [formula omitted]-path vertex cover | Graph products | k-path vertex cover | MATHEMATICS | TERMS | BIPARTITE GRAPHS

Vertex cover | Dissociation number | Independence number | [formula omitted]-path vertex cover | Graph products | k-path vertex cover | MATHEMATICS | TERMS | BIPARTITE GRAPHS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 07/2016, Volume 339, Issue 7, pp. 1935 - 1939

The 3-path vertex cover problem is an extension of the well-known vertex cover problem. It asks for a vertex set S⊆V(G) of minimum cardinality such that G−S...

Vertex cover | Crown reduction | [formula omitted]-path vertex cover | Kernelization | k-path vertex cover | MATHEMATICS | P-3 PROBLEM | APPROXIMATION ALGORITHM | GRAPHS

Vertex cover | Crown reduction | [formula omitted]-path vertex cover | Kernelization | k-path vertex cover | MATHEMATICS | P-3 PROBLEM | APPROXIMATION ALGORITHM | GRAPHS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2017, Volume 223, pp. 28 - 38

The minimum vertex cover problem and the minimum vertex partition problem are central problems in graph theory and many generalisations are known. Two examples...

Forbidden subgraphs | [formula omitted]-path partition | [formula omitted]-path vertex cover | k-path partition | k-path vertex cover | MATHEMATICS, APPLIED | P-3 PROBLEM | APPROXIMATION ALGORITHM | DISSOCIATION NUMBER | BIPARTITE GRAPHS | Computer science | Hardness | Algebra

Forbidden subgraphs | [formula omitted]-path partition | [formula omitted]-path vertex cover | k-path partition | k-path vertex cover | MATHEMATICS, APPLIED | P-3 PROBLEM | APPROXIMATION ALGORITHM | DISSOCIATION NUMBER | BIPARTITE GRAPHS | Computer science | Hardness | Algebra

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2015, Volume 187, pp. 111 - 119

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 ψk(G) the...

Vertex cover | Rooted product | Dissociation number | Independence number | [formula omitted]-path vertex cover | k-path vertex cover | MATHEMATICS, APPLIED | P-3 PROBLEM | TERMS | APPROXIMATION ALGORITHM | BIPARTITE GRAPHS

Vertex cover | Rooted product | Dissociation number | Independence number | [formula omitted]-path vertex cover | k-path vertex cover | MATHEMATICS, APPLIED | P-3 PROBLEM | TERMS | APPROXIMATION ALGORITHM | BIPARTITE GRAPHS

Journal Article

Information Processing Letters, ISSN 0020-0190, 03/2017, Volume 119, pp. 9 - 13

•We studied the minimum k-path vertex cover problem (VCPk) in ball graph for general k.•A PTAS for VCPk is presented for a ball graph with bounded...

Approximation algorithms | PTAS | k-path vertex cover | Ball graph | SET | P-3 PROBLEM | COMPUTER SCIENCE, INFORMATION SYSTEMS | APPROXIMATION ALGORITHM | CUBIC GRAPHS | DELETION

Approximation algorithms | PTAS | k-path vertex cover | Ball graph | SET | P-3 PROBLEM | COMPUTER SCIENCE, INFORMATION SYSTEMS | APPROXIMATION ALGORITHM | CUBIC GRAPHS | DELETION

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 08/2018, Volume 331, pp. 69 - 79

For a graph G and a positive integer k, a subset S of vertices of G is called a k-path vertex cover if S intersects all paths of order k in G. The cardinality...

Lexicographic product | Strong product | k-path vertex cover | Complete bipartite graph | Cartesian product | MATHEMATICS, APPLIED | INDEPENDENCE NUMBER | P-3 PROBLEM | APPROXIMATION ALGORITHM | DISSOCIATION NUMBER

Lexicographic product | Strong product | k-path vertex cover | Complete bipartite graph | Cartesian product | MATHEMATICS, APPLIED | INDEPENDENCE NUMBER | P-3 PROBLEM | APPROXIMATION ALGORITHM | DISSOCIATION NUMBER

Journal Article

10.
Full Text
A simpler PTAS for connected k-path vertex cover in homogeneous wireless sensor network

Journal of Combinatorial Optimization, ISSN 1382-6905, 7/2018, Volume 36, Issue 1, pp. 35 - 43

Because of its application in the field of security in wireless sensor networks, k-path vertex cover ($$\hbox {VCP}_k$$ VCPk ) has received a lot of attention...

PTAS | Convex and Discrete Geometry | Operations Research/Decision Theory | Connected k -path vertex cover | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Combinatorics | Approximation algorithm | Optimization | Unit disk graph | Connected k-path vertex cover | DOMINATING SET | MINIMUM | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | P-3 PROBLEM | ALGORITHMS | GRAPHS | Wireless sensor networks | Algorithms | Sensors | Analysis

PTAS | Convex and Discrete Geometry | Operations Research/Decision Theory | Connected k -path vertex cover | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Combinatorics | Approximation algorithm | Optimization | Unit disk graph | Connected k-path vertex cover | DOMINATING SET | MINIMUM | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | P-3 PROBLEM | ALGORITHMS | GRAPHS | Wireless sensor networks | Algorithms | Sensors | Analysis

Journal Article

Journal of Global Optimization, ISSN 0925-5001, 06/2013, Volume 56, Issue 2, pp. 449 - 458

In the Minimum k-Path Connected Vertex Cover Problem (MkPCVCP), we are given a connected graph G and an integer k a parts per thousand yen 2, and are required...

k-Path connected vertex cover | Unit disk graph | PTAS | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION SCHEME | PROTOCOL | NETWORKS | Computer science | Studies | Graph theory | Analysis | Optimization | Remote sensors | Approximation | Wireless networks | Mathematical analysis | Disks | Graphs | Polynomials

k-Path connected vertex cover | Unit disk graph | PTAS | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | APPROXIMATION SCHEME | PROTOCOL | NETWORKS | Computer science | Studies | Graph theory | Analysis | Optimization | Remote sensors | Approximation | Wireless networks | Mathematical analysis | Disks | Graphs | Polynomials

Journal Article

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2014, Volume 8881, pp. 764 - 771

Journal Article

Global Journal of Pure and Applied Mathematics, ISSN 0973-1768, 2016, Volume 12, Issue 2, pp. 1403 - 1412

Journal Article

Journal of Graph Theory, ISSN 0364-9024, 05/2019, Volume 91, Issue 1, pp. 73 - 87

The famous Kőnig‐Egerváry theorem is equivalent to the statement that the matching number equals the vertex cover number for every induced subgraph of some...

vertex cover | Kőnig‐Egerváry theorem | bipartite graph | k‐path vertex cover | matching | k-path vertex cover | Kőnig-Egerváry theorem | MATHEMATICS | Konig-Egervary theorem | 3-PATH VERTEX COVER | ALGORITHMS | DISSOCIATION NUMBER | Mathematics | Combinatorics | Computer Science | Discrete Mathematics

vertex cover | Kőnig‐Egerváry theorem | bipartite graph | k‐path vertex cover | matching | k-path vertex cover | Kőnig-Egerváry theorem | MATHEMATICS | Konig-Egervary theorem | 3-PATH VERTEX COVER | ALGORITHMS | DISSOCIATION NUMBER | Mathematics | Combinatorics | Computer Science | Discrete Mathematics

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 05/2014, Volume 535, pp. 54 - 58

A subset F of vertices is called a connected k-subgraph cover (VCCk) if every connected subgraph on k vertices contains at least one vertex from F. The minimum...

k-Path vertex cover | Connected k-subgraph vertex cover | Algorithms

k-Path vertex cover | Connected k-subgraph vertex cover | Algorithms

Journal Article

16.
Full Text
A simpler method to obtain a PTAs for connected k-path vertex cover in unit disk graph

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2017, Volume 10251, pp. 584 - 592

Conference Proceeding

Discrete Applied Mathematics, ISSN 0166-218X, 04/2018, Volume 239, pp. 119 - 124

For a set H of graphs, a graph G is H-free if G does not contain any subgraph isomorphic to some graph in H. In this paper, we study the minimum H-free node...

Node deletion problem | Local search | PTAS | Degree-bounded node deletion | Disk graph | Maximum subgraph problem | Connected [formula omitted]-subgraph cover | [formula omitted]-path vertex cover | Connected k-subgraph cover | k-path vertex cover | MATHEMATICS, APPLIED | SET | PATH VERTEX COVER | P-3 PROBLEM | APPROXIMATION ALGORITHM | CUBIC GRAPHS | BIPARTITE GRAPHS

Node deletion problem | Local search | PTAS | Degree-bounded node deletion | Disk graph | Maximum subgraph problem | Connected [formula omitted]-subgraph cover | [formula omitted]-path vertex cover | Connected k-subgraph cover | k-path vertex cover | MATHEMATICS, APPLIED | SET | PATH VERTEX COVER | P-3 PROBLEM | APPROXIMATION ALGORITHM | CUBIC GRAPHS | BIPARTITE GRAPHS

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 07/2019, Volume 352, pp. 211 - 219

Vertex cover number, which is one of the most basic graph invariants, can be viewed as the smallest number of vertices that hit (or that belong to) every...

Hitting set | k-path vertex cover | tidy graph | Decycling number | Quasi-spider | MATHEMATICS, APPLIED | P-4-tidy graph | PATH VERTEX COVER | COMPLEXITY | DISSOCIATION NUMBER

Hitting set | k-path vertex cover | tidy graph | Decycling number | Quasi-spider | MATHEMATICS, APPLIED | P-4-tidy graph | PATH VERTEX COVER | COMPLEXITY | DISSOCIATION NUMBER

Journal Article

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2014, Volume 8630, Issue 1, pp. 114 - 126

Conference Proceeding

Applied Mathematics and Computation, ISSN 0096-3003, 07/2019, Volume 352, pp. 211 - 219

Vertex cover number, which is one of the most basic graph invariants, can be viewed as the smallest number of vertices that hit (or that belong to) every...

Hitting set | k-path vertex cover | Decycling number | P4-tidy graph | Quasi-spider

Hitting set | k-path vertex cover | Decycling number | P4-tidy graph | Quasi-spider

Journal Article

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