Algorithmica, ISSN 0178-4617, 2/2016, Volume 74, Issue 2, pp. 602 - 629

We show that the following two problems are fixed-parameter tractable with parameter $$k$$ k : testing whether a connected $$n$$ n -vertex graph with $$m$$ m...

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | Graph square root | Theory of Computation | Algorithm Analysis and Problem Complexity | Generalized kernel | Parameterized complexity | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Computational Complexity

Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | Graph square root | Theory of Computation | Algorithm Analysis and Problem Complexity | Generalized kernel | Parameterized complexity | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | Computational Complexity

Journal Article

PLOS ONE, ISSN 1932-6203, 10/2018, Volume 13, Issue 10, p. e0205820

A common two-tier structure for social networks is based on partitioning society into two parts, referred to as the elite and the periphery, where the “elite”...

Social network analysis | Social networks | Nodes | Scientometrics | Distributed processing | Partitions | Social interactions | Axioms | Information sharing | Data collection | Social organization | Society | Books | Power

Social network analysis | Social networks | Nodes | Scientometrics | Distributed processing | Partitions | Social interactions | Axioms | Information sharing | Data collection | Social organization | Society | Books | Power

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 03/2019, Volume 257, pp. 158 - 174

The square of a given graph H=(V,E) is obtained from H by adding an edge between every two vertices at distance two in H. Given a graph class H, the H-Square...

Cactus-block graphs | Square root of a graph | Cycle-power graphs | Clique-separator decomposition | Cut-vertices | MATHEMATICS, APPLIED | DECOMPOSITION | ALGORITHMS | POWERS | Algorithms | Research institutes | Apexes | Roots | Graphs | Trees (mathematics) | Graph theory | Polynomials | Decomposition | Recognition | Data Structures and Algorithms | Computer Science | Computational Complexity | Discrete Mathematics

Cactus-block graphs | Square root of a graph | Cycle-power graphs | Clique-separator decomposition | Cut-vertices | MATHEMATICS, APPLIED | DECOMPOSITION | ALGORITHMS | POWERS | Algorithms | Research institutes | Apexes | Roots | Graphs | Trees (mathematics) | Graph theory | Polynomials | Decomposition | Recognition | Data Structures and Algorithms | Computer Science | Computational Complexity | Discrete Mathematics

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 10/2018, Volume 248, pp. 93 - 101

A graph H is a square root of a graph G if G can be obtained from H by adding an edge between any two vertices in H that are of distance 2. The Square Root...

Square root | Polynomial algorithm | Bounded degree graph | MATHEMATICS, APPLIED | SPLIT GRAPHS | LOGIC | Computer Science | Computational Complexity

Square root | Polynomial algorithm | Bounded degree graph | MATHEMATICS, APPLIED | SPLIT GRAPHS | LOGIC | Computer Science | Computational Complexity

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2014, Volume 168, pp. 34 - 39

Let G be a graph class. The square root of G contains all graphs whose squares belong in G. We prove that if G is non-trivial and minor closed, then all graphs...

Carving-width | Square roots of graphs | Graph minors | Branch-width | MATHEMATICS, APPLIED | CONTAINMENT | ALGORITHMS | Algorithms | Graphs | Mathematical analysis | Roots | Recognition | Computer Science | Discrete Mathematics

Carving-width | Square roots of graphs | Graph minors | Branch-width | MATHEMATICS, APPLIED | CONTAINMENT | ALGORITHMS | Algorithms | Graphs | Mathematical analysis | Roots | Recognition | Computer Science | Discrete Mathematics

Journal Article

Computer Aided Geometric Design, ISSN 0167-8396, 08/2017, Volume 56, pp. 52 - 66

In this paper we study situations when non-rational parameterizations of planar or space curves as results of certain geometric operations or constructions are...

Weierstrass form | Hyperelliptic curves | Rational approximation | Topological graph | Square-root parameterization | MATHEMATICS, APPLIED | ALGEBRAIC SPACE-CURVES | OFFSET CURVES | BISECTOR | COMPUTER SCIENCE, SOFTWARE ENGINEERING | CONTOUR CURVES | HYPERSURFACES | LAGUERRE GEOMETRY | CANAL SURFACES | Analysis | Algorithms

Weierstrass form | Hyperelliptic curves | Rational approximation | Topological graph | Square-root parameterization | MATHEMATICS, APPLIED | ALGEBRAIC SPACE-CURVES | OFFSET CURVES | BISECTOR | COMPUTER SCIENCE, SOFTWARE ENGINEERING | CONTOUR CURVES | HYPERSURFACES | LAGUERRE GEOMETRY | CANAL SURFACES | Analysis | Algorithms

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 07/2013, Volume 161, Issue 10-11, pp. 1538 - 1545

A graph H is a square root of a graph G if two vertices are adjacent in G if and only if they are at distance one or two in H. Computing a square root of a...

Linear time algorithm | Chordal graph | Split graph | Trivially perfect graph | Threshold graph | Square root of a graph | Square of a graph | MATHEMATICS, APPLIED | NLC-WIDTH | POWERS | Algorithms | Thresholds | Computation | Roots | Graphs | Mathematical models | Computing time | Structural analysis

Linear time algorithm | Chordal graph | Split graph | Trivially perfect graph | Threshold graph | Square root of a graph | Square of a graph | MATHEMATICS, APPLIED | NLC-WIDTH | POWERS | Algorithms | Thresholds | Computation | Roots | Graphs | Mathematical models | Computing time | Structural analysis

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 08/2017, Volume 689, pp. 36 - 47

A graph H is a square root of a graph G if G can be obtained from H by the addition of edges between any two vertices in H that are at distance 2 from each...

Square root | k-apex graphs | Linear kernel | COMPUTER SCIENCE, THEORY & METHODS | SPLIT

Square root | k-apex graphs | Linear kernel | COMPUTER SCIENCE, THEORY & METHODS | SPLIT

Journal Article

Theory of Computing Systems, ISSN 1432-4350, 8/2018, Volume 62, Issue 6, pp. 1409 - 1426

A graph H is a square root of a graph G, or equivalently, G is the square of H, if G can be obtained from H by adding an edge between any two vertices in H...

Theory of Computation | Clique number | Square root | Computer Science | Cactus | Treewidth | MATHEMATICS | SQUARE ROOTS | COMPUTER SCIENCE, THEORY & METHODS | SPLIT GRAPHS | Computer science | Computational mathematics | Graph theory | Polynomials | Algorithms

Theory of Computation | Clique number | Square root | Computer Science | Cactus | Treewidth | MATHEMATICS | SQUARE ROOTS | COMPUTER SCIENCE, THEORY & METHODS | SPLIT GRAPHS | Computer science | Computational mathematics | Graph theory | Polynomials | Algorithms

Journal Article

Algorithmica, ISSN 0178-4617, 2/2015, Volume 71, Issue 2, pp. 471 - 495

Let T be a tree on a set V of nodes. The p-th power T p of T is the graph on V such that any two nodes u and w of V are adjacent in T p if and only if the...

Graph root | Minimal node separator | Tree root | Graph power | Chordal graph | Theory of Computation | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Maximal clique | Mathematics of Computing | Computer Science | Tree power | Algorithm Analysis and Problem Complexity | INTERVAL-GRAPHS | MATHEMATICS, APPLIED | SQUARE | CHROMATIC NUMBER | INDEPENDENT SETS | GRAPH POWERS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SEPARATORS | CHORDAL GRAPHS | PLANAR GRAPHS | Computer science

Graph root | Minimal node separator | Tree root | Graph power | Chordal graph | Theory of Computation | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Maximal clique | Mathematics of Computing | Computer Science | Tree power | Algorithm Analysis and Problem Complexity | INTERVAL-GRAPHS | MATHEMATICS, APPLIED | SQUARE | CHROMATIC NUMBER | INDEPENDENT SETS | GRAPH POWERS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | SEPARATORS | CHORDAL GRAPHS | PLANAR GRAPHS | Computer science

Journal Article

Leibniz International Proceedings in Informatics, LIPIcs, ISSN 1868-8969, 06/2016, Volume 53, pp. 4.1 - 4.14

Conference Proceeding

SIAM Journal on Computing, ISSN 0097-5397, 2010, Volume 39, Issue 5, pp. 1748 - 1771

This paper shows how to compute ... to the Sparsest Cut and Balanced Separator problems in ... time, thus improving upon the recent algorithm of Arora, Rao,...

Graph partitioning | Expander flows | Multiplicative weights | Studies | Semidefinite programming | Computational mathematics

Graph partitioning | Expander flows | Multiplicative weights | Studies | Semidefinite programming | Computational mathematics

Journal Article

Electronic Notes in Discrete Mathematics, ISSN 1571-0653, 11/2016, Volume 55, pp. 195 - 198

The Square Root problem is that of deciding whether a given graph admits a square root. This problem is only known to be NP-complete for chordal graphs and...

squares | square roots | graph classes | treewidth

squares | square roots | graph classes | treewidth

Journal Article

Algorithmica, ISSN 0178-4617, 2/2012, Volume 62, Issue 1, pp. 38 - 53

Graph G is the square of graph H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Given H it is easy to compute its...

Recognition algorithms | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Graph powers | Computer Science | NP-completeness | Theory of Computation | Algorithm Analysis and Problem Complexity | Graph roots | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SQUARE | ALGORITHMS | POWERS | Computer science

Recognition algorithms | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Graph powers | Computer Science | NP-completeness | Theory of Computation | Algorithm Analysis and Problem Complexity | Graph roots | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | SQUARE | ALGORITHMS | POWERS | Computer science

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 10/2016, Volume 648, pp. 26 - 33

The square of a graph G, denoted by G2, is obtained from G by putting an edge between two distinct vertices whenever their distance is two. Then G is called a...

Square of graphs | Square of split graphs | ROOTS | COMPUTER SCIENCE, THEORY & METHODS | Algorithms | Theorems | Roots | Graphs | Polynomials | Graph theory | Cases (containers) | Dichotomies

Square of graphs | Square of split graphs | ROOTS | COMPUTER SCIENCE, THEORY & METHODS | Algorithms | Theorems | Roots | Graphs | Polynomials | Graph theory | Cases (containers) | Dichotomies

Journal Article

IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, ISSN 1057-7122, 12/2002, Volume 49, Issue 12, pp. 1702 - 1712

A new systematic design procedure for square-root-domain (/spl radic/x-domain) circuits, which is based on the signal flow graph (SFG) synthesis approach, is...

Low pass filters | Circuit simulation | Prototypes | Chebyshev approximation | Circuit synthesis | Complexity theory | Flow graphs | Signal synthesis | Signal design | Immune system | Active filter | Translinear circuits | Square-root-domain (√x-domain) circuits | Analog integrated circuits | INTEGRATOR | square-root-domain (root x-domain) circuits | translinear circuits | analog integrated circuits | FILTERS | active filter | PRINCIPLE | STATE-SPACE | ENGINEERING, ELECTRICAL & ELECTRONIC

Low pass filters | Circuit simulation | Prototypes | Chebyshev approximation | Circuit synthesis | Complexity theory | Flow graphs | Signal synthesis | Signal design | Immune system | Active filter | Translinear circuits | Square-root-domain (√x-domain) circuits | Analog integrated circuits | INTEGRATOR | square-root-domain (root x-domain) circuits | translinear circuits | analog integrated circuits | FILTERS | active filter | PRINCIPLE | STATE-SPACE | ENGINEERING, ELECTRICAL & ELECTRONIC

Journal Article

Journal of Algebra, ISSN 0021-8693, 03/2015, Volume 425, pp. 146 - 178

Let Λ be a basic finite dimensional algebra over an algebraically closed field, with the property that the square of the Jacobson radical J vanishes. We...

Representations of finite dimensional algebras | Irreducible components of parametrizing varieties | Generic properties of representations | MATHEMATICS | REPRESENTATION-THEORY | QUIVERS | MATRICES | VARIETIES | INFINITE ROOT SYSTEMS | IRREDUCIBLE COMPONENTS | INVARIANT-THEORY | GRAPHS | Algebra

Representations of finite dimensional algebras | Irreducible components of parametrizing varieties | Generic properties of representations | MATHEMATICS | REPRESENTATION-THEORY | QUIVERS | MATRICES | VARIETIES | INFINITE ROOT SYSTEMS | IRREDUCIBLE COMPONENTS | INVARIANT-THEORY | GRAPHS | Algebra

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 10/2018, Volume 248, p. 93

A graph H is a square root of a graph G if G can be obtained from H by adding an edge between any two vertices in H that are of distance 2. The Square Root...

Mathematical problems | Graphs | Graph theory | Mathematics | Polynomials

Mathematical problems | Graphs | Graph theory | Mathematics | Polynomials

Journal Article

19.
Full Text
Polynomial time recognition of squares of Ptolemaic graphs and 3-sun-free split graphs

Theoretical Computer Science, ISSN 0304-3975, 10/2015, Volume 602, pp. 39 - 49

The square of a graph G, denoted G2, is obtained from G by putting an edge between two distinct vertices whenever their distance is two. Then G is called a...

Square of Ptolemaic graph | Square of graph | Recognition algorithm | Square of split graph | ROOTS | COMPUTER SCIENCE, THEORY & METHODS | POWERS | Algorithms | Graphs | Polynomials | Graph theory | Roots | Recognition

Square of Ptolemaic graph | Square of graph | Recognition algorithm | Square of split graph | ROOTS | COMPUTER SCIENCE, THEORY & METHODS | POWERS | Algorithms | Graphs | Polynomials | Graph theory | Roots | Recognition

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 08/2014, Volume 173, pp. 83 - 91

The square of a graph G, denoted by G2, is the graph obtained from G by putting an edge between two distinct vertices whenever their distance in G is at most...

Linear time algorithm | The square of a graph | Line graph | MATHEMATICS, APPLIED | ROOTS | Algorithms | Mathematical analysis | Graphs

Linear time algorithm | The square of a graph | Line graph | MATHEMATICS, APPLIED | ROOTS | Algorithms | Mathematical analysis | Graphs

Journal Article