Theoretical Computer Science, ISSN 0304-3975, 10/2015, Volume 600, pp. 49 - 58

In this paper, we prove several inapproximability results on the -convexity and the geodesic convexity in graphs. We prove that determining the -hull number...

Inapproximability results | Geodesic convexity | Radon number | APX-hardness | Carathéodory number | Hull number | [formula omitted]-convexity | P 3 -convexity | Caratheodory number | PATHS | ORDER 3 | COMPUTER SCIENCE, THEORY & METHODS | P-3-convexity | Intervals | Radon | Graphs | Polynomials | Convexity | Hulls (structures) | Hulls

Inapproximability results | Geodesic convexity | Radon number | APX-hardness | Carathéodory number | Hull number | [formula omitted]-convexity | P 3 -convexity | Caratheodory number | PATHS | ORDER 3 | COMPUTER SCIENCE, THEORY & METHODS | P-3-convexity | Intervals | Radon | Graphs | Polynomials | Convexity | Hulls (structures) | Hulls

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 06/2016, Volume 206, pp. 39 - 47

In a of a graph no edges exist joining vertices and such that . A set is , or - , if the vertices of every triangle path joining two vertices of are in . The...

Convexity number | Graph convexity | Hull number | Triangle path convexity | MATHEMATICS, APPLIED | DECOMPOSITION | P-3-RADON NUMBER | ORDER 3 | CLIQUE SEPARATORS | GRAPHS | Triangles | Graphs | Joining | Graph theory | Convexity | Hulls (structures) | Hulls | Complexity

Convexity number | Graph convexity | Hull number | Triangle path convexity | MATHEMATICS, APPLIED | DECOMPOSITION | P-3-RADON NUMBER | ORDER 3 | CLIQUE SEPARATORS | GRAPHS | Triangles | Graphs | Joining | Graph theory | Convexity | Hulls (structures) | Hulls | Complexity

Journal Article

The Economic Journal, ISSN 0013-0133, 03/2015, Volume 125, Issue 583, pp. 574 - 620

‘To slow or not to slow’ (Nordhaus, 1991) was the first economic appraisal of greenhouse gas emissions abatement and founded a large literature on a topic of...

CONTROLLING GREENHOUSE GASES | OPTIMAL TRANSITION PATH | CHANGE POLICY | TARGETS | ECONOMICS | ECONOMIC-GROWTH | SCIENCE | EQUITY | DICE MODEL | ETHICS | Air quality management | Emissions (Pollution) | Air pollution | Studies | Economic models | Emissions control | Environmental policy | Economic growth

CONTROLLING GREENHOUSE GASES | OPTIMAL TRANSITION PATH | CHANGE POLICY | TARGETS | ECONOMICS | ECONOMIC-GROWTH | SCIENCE | EQUITY | DICE MODEL | ETHICS | Air quality management | Emissions (Pollution) | Air pollution | Studies | Economic models | Emissions control | Environmental policy | Economic growth

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 10/2013, Volume 510, pp. 127 - 135

Inspired by a result of Carathéodory [Über den Variabilitätsbereich der Fourierschen Konstanten von positiven harmonischen Funktionen, Rend. Circ. Mat. Palermo...

Convexity space | Interval convexity | Carathéodory number | [formula omitted]-convexity | Monophonic convexity | Geodetic convexity | convexity | Caratheodory number | SETS | ORDER 3 | COMPUTER SCIENCE, THEORY & METHODS | PATH CONVEXITY | P-3-convexity | HULL NUMBER | Hardness

Convexity space | Interval convexity | Carathéodory number | [formula omitted]-convexity | Monophonic convexity | Geodetic convexity | convexity | Caratheodory number | SETS | ORDER 3 | COMPUTER SCIENCE, THEORY & METHODS | PATH CONVEXITY | P-3-convexity | HULL NUMBER | Hardness

Journal Article

DISCRETE APPLIED MATHEMATICS, ISSN 0166-218X, 12/2018, Volume 251, pp. 245 - 257

Recent papers investigated the maximum infection times t(p3)(G), t(gd)(G) and t(mo)(G) of the P3 convexity, geodesic convexity and monophonic convexity,...

MATHEMATICS, APPLIED | THRESHOLD | NUMBER | BOOTSTRAP PERCOLATION | Maximum infection time | PATHS | Graph convexity | P-3 convexity

MATHEMATICS, APPLIED | THRESHOLD | NUMBER | BOOTSTRAP PERCOLATION | Maximum infection time | PATHS | Graph convexity | P-3 convexity

Journal Article

DISCRETE APPLIED MATHEMATICS, ISSN 0166-218X, 07/2014, Volume 172, pp. 104 - 108

If S is a set of vertices of a graph G, then the convex hull of S in the P-3 convexity of G is the smallest set T of vertices of G that contains S and that has...

Caratheodory number | PATHS | MATHEMATICS, APPLIED | P-3 convexity | HULL NUMBER | SETS | Algorithms

Caratheodory number | PATHS | MATHEMATICS, APPLIED | P-3 convexity | HULL NUMBER | SETS | Algorithms

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 09/2015, Volume 192, pp. 28 - 39

A graph is (q,q-4) if every subset of at most q vertices induces at most q-4 P4 's. It therefore generalizes some different classes, as cographs and P4 -sparse...

Radon number | Carathéodory number | Convexity of paths of order three | Hull number | (q, q - 4) -graphs | Fixed parameter tractability | Algorithms

Radon number | Carathéodory number | Convexity of paths of order three | Hull number | (q, q - 4) -graphs | Fixed parameter tractability | Algorithms

Journal Article

DISCRETE APPLIED MATHEMATICS, ISSN 0166-218X, 09/2015, Volume 192, pp. 28 - 39

A graph is (q, q-4) if every subset of at most q vertices induces at most q-4P(4)'s. It therefore generalizes some different classes, as cographs and...

Caratheodory number | MATHEMATICS, APPLIED | BEHAVIOR | Radon number | Convexity of paths of order three | ALGORITHMS | Hull number | (q, q-4)-graphs | Fixed parameter tractability

Caratheodory number | MATHEMATICS, APPLIED | BEHAVIOR | Radon number | Convexity of paths of order three | ALGORITHMS | Hull number | (q, q-4)-graphs | Fixed parameter tractability

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 5/2012, Volume 28, Issue 3, pp. 333 - 345

A set of vertices S in a graph is convex if it contains all vertices which belong to shortest paths between vertices in S. The convexity number c(G) of a graph...

Convex hull | Convex set | Graph | Shortest path | Convexity number | Mathematics | Engineering Design | Combinatorics | MATHEMATICS | SETS | Graphs | Theorems | Integers | Convexity | Upper bounds | Combinatorial analysis | Shortest-path problems

Convex hull | Convex set | Graph | Shortest path | Convexity number | Mathematics | Engineering Design | Combinatorics | MATHEMATICS | SETS | Graphs | Theorems | Integers | Convexity | Upper bounds | Combinatorial analysis | Shortest-path problems

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2011, Volume 227, Issue 1, pp. 210 - 244

Affine buildings are in a certain sense analogs of symmetric spaces. It is therefore natural to ask for analogs of results for symmetric spaces. We prove a...

Affine buildings | Convexity | Combinatorics | BN-pairs | Λ-metric spaces | Retractions | MATHEMATICS | REPRESENTATION-THEORY | Lambda-metric spaces | PATH MODEL

Affine buildings | Convexity | Combinatorics | BN-pairs | Λ-metric spaces | Retractions | MATHEMATICS | REPRESENTATION-THEORY | Lambda-metric spaces | PATH MODEL

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 09/2015, Volume 192, pp. 28 - 39

A graph is if every subset of at most vertices induces at most ’s. It therefore generalizes some different classes, as cographs and -sparse graphs. In this...

Radon number | Convexity of paths of order three | Carathéodory number | Hull number | [formula omitted]-graphs | Fixed parameter tractability

Radon number | Convexity of paths of order three | Carathéodory number | Hull number | [formula omitted]-graphs | Fixed parameter tractability

Journal Article

Journal of Algebraic Combinatorics, ISSN 0925-9899, 11/2010, Volume 32, Issue 3, pp. 303 - 338

We prove two recent conjectures of Liu and Wang by establishing the strong q-log-convexity of the Narayana polynomials, and showing that the Narayana...

Mathematics | Schur positivity | Lattice permutation | q -Log-convexity | Littlewood–Richardson rule | Convex and Discrete Geometry | q -Narayana number | Narayana polynomial | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | q -Log-concavity | Computer Science, general | Combinatorics | Littlewood-Richardson rule | q-Narayana number | q-Log-concavity | q-Log-convexity | CONCAVITY | NUMBERS | SEQUENCES | BINOMIAL COEFFICIENTS | CATALAN PATH STATISTICS | LITTLEWOOD-RICHARDSON COEFFICIENTS | MATHEMATICS | COMBINATORICS

Mathematics | Schur positivity | Lattice permutation | q -Log-convexity | Littlewood–Richardson rule | Convex and Discrete Geometry | q -Narayana number | Narayana polynomial | Group Theory and Generalizations | Order, Lattices, Ordered Algebraic Structures | q -Log-concavity | Computer Science, general | Combinatorics | Littlewood-Richardson rule | q-Narayana number | q-Log-concavity | q-Log-convexity | CONCAVITY | NUMBERS | SEQUENCES | BINOMIAL COEFFICIENTS | CATALAN PATH STATISTICS | LITTLEWOOD-RICHARDSON COEFFICIENTS | MATHEMATICS | COMBINATORICS

Journal Article

Acta Applicandae Mathematicae, ISSN 0167-8019, 6/2010, Volume 110, Issue 3, pp. 1373 - 1392

Three new methods for proving log-convexity of combinatorial sequences are presented. Their implementation is demonstrated and their performance is compared...

Schröder numbers | Motzkin numbers | 05B50 | Theoretical, Mathematical and Computational Physics | 05A20 | Lattice paths | Mathematics | Statistical Physics, Dynamical Systems and Complexity | Integer sequences | Recurrences | 11B37 | Delannoy numbers | 11B83 | Mechanics | Mathematics, general | 26A17 | Catalan numbers | Computer Science, general | Log-convexity | 05E35 | DRUG | MATHEMATICS, APPLIED | PROOFS | CONCAVITY | Schroder numbers | COMBINATORIAL SEQUENCES | DISPOSITION CURVES | Universities and colleges | Studies | Mathematical analysis

Schröder numbers | Motzkin numbers | 05B50 | Theoretical, Mathematical and Computational Physics | 05A20 | Lattice paths | Mathematics | Statistical Physics, Dynamical Systems and Complexity | Integer sequences | Recurrences | 11B37 | Delannoy numbers | 11B83 | Mechanics | Mathematics, general | 26A17 | Catalan numbers | Computer Science, general | Log-convexity | 05E35 | DRUG | MATHEMATICS, APPLIED | PROOFS | CONCAVITY | Schroder numbers | COMBINATORIAL SEQUENCES | DISPOSITION CURVES | Universities and colleges | Studies | Mathematical analysis

Journal Article

SIAM JOURNAL ON DISCRETE MATHEMATICS, ISSN 0895-4801, 2013, Volume 27, Issue 2, pp. 717 - 731

We study the graphs G for which the hull number h(G) and the geodetic number g(G) with respect to P-3-convexity coincide. These two parameters correspond to...

MATHEMATICS, APPLIED | PERCOLATION | PATHS | geodetic number | ORDER 3 | hull number | COALITIONS | P-3-convexity | irreversible 2-threshold processes | GRAPHS | Construction | Mathematical analysis | Graphs | Hulls (structures) | Hulls | Iterative methods | Character recognition | Recognition

MATHEMATICS, APPLIED | PERCOLATION | PATHS | geodetic number | ORDER 3 | hull number | COALITIONS | P-3-convexity | irreversible 2-threshold processes | GRAPHS | Construction | Mathematical analysis | Graphs | Hulls (structures) | Hulls | Iterative methods | Character recognition | Recognition

Journal Article

European Journal of Combinatorics, ISSN 0195-6698, 2008, Volume 29, Issue 3, pp. 641 - 651

In the context of two-path convexity, we study the , and for multipartite tournaments. We show the maximum Caratheodory number of a multipartite tournament is...

MATHEMATICS | PATH CONVEXITY | GRAPHS

MATHEMATICS | PATH CONVEXITY | GRAPHS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2011, Volume 311, Issue 8, pp. 616 - 619

A finite convexity space is a pair consisting of a finite set and a set of subsets of such that , , and is closed under intersection. A graph with vertex set...

Convexity space | All-path convexity | Monophonic convexity | Triangle-path convexity | Geodetic convexity | MATHEMATICS | BETWEENNESS | Algorithms | Mathematical analysis | Images | Graphs | Convexity | Hulls | Hulls (structures) | Intersections

Convexity space | All-path convexity | Monophonic convexity | Triangle-path convexity | Geodetic convexity | MATHEMATICS | BETWEENNESS | Algorithms | Mathematical analysis | Images | Graphs | Convexity | Hulls | Hulls (structures) | Intersections

Journal Article

Computational Mechanics, ISSN 0178-7675, 10/2008, Volume 42, Issue 5, pp. 685 - 694

Yield surfaces for unsaturated soils are usually non-convex if the size of the yield surface has to increase with increasing suction. An expanding yield...

Non-convex yield surface | Engineering | Mechanics, Fluids, Thermodynamics | Differential algebraic system | Runge–Kutta method | Stress update | Numerical integration | Unsaturated soils | Path dependent hardening | Computational Science and Engineering | Theoretical and Applied Mechanics | Runge-Kutta method | unsaturated soils | non-convex yield surface | numerical integration | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | INTEGRATION | path dependent hardening | CONSTITUTIVE MODEL | ELASTOPLASTICITY | stress update | differential algebraic system | Finite element method | Collapse | Soil stresses | Wetting | Soil suction | Dependence | Mathematical models | Constitutive models | Convexity

Non-convex yield surface | Engineering | Mechanics, Fluids, Thermodynamics | Differential algebraic system | Runge–Kutta method | Stress update | Numerical integration | Unsaturated soils | Path dependent hardening | Computational Science and Engineering | Theoretical and Applied Mechanics | Runge-Kutta method | unsaturated soils | non-convex yield surface | numerical integration | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | INTEGRATION | path dependent hardening | CONSTITUTIVE MODEL | ELASTOPLASTICITY | stress update | differential algebraic system | Finite element method | Collapse | Soil stresses | Wetting | Soil suction | Dependence | Mathematical models | Constitutive models | Convexity

Journal Article

Filomat, ISSN 0354-5180, 1/2015, Volume 29, Issue 9, pp. 2097 - 2105

In this paper, without assumption of monotonicity and boundedness, we study existence results for a solution and the convexity of the solution set to the...

Nash equilibrium | Mathematical vectors | Convexity | Variational inequalities | GENERALIZED MONOTONE BIFUNCTIONS | SYSTEM | EXISTENCE | MATHEMATICS, APPLIED | MULTIVALUED MAPPINGS | VARIATIONAL INEQUALITY | convexity | Symmetric vector equilibrium problem | MATHEMATICS | FIXED-POINT THEOREMS | KKM map | SCALARIZATION | connectedness | path-connectedness | EFFICIENT SOLUTIONS

Nash equilibrium | Mathematical vectors | Convexity | Variational inequalities | GENERALIZED MONOTONE BIFUNCTIONS | SYSTEM | EXISTENCE | MATHEMATICS, APPLIED | MULTIVALUED MAPPINGS | VARIATIONAL INEQUALITY | convexity | Symmetric vector equilibrium problem | MATHEMATICS | FIXED-POINT THEOREMS | KKM map | SCALARIZATION | connectedness | path-connectedness | EFFICIENT SOLUTIONS

Journal Article

Journal of Optimization Theory and Applications, ISSN 0022-3239, 10/2005, Volume 127, Issue 1, pp. 165 - 176

Some properties of the spaces of paths are studied in order to define and characterize the local convexity of sets belonging to smooth manifolds and the local...

space of paths | linear connections | Operations Research/Decision Theory | local convexity | Calculus of Variations and Optimal Control | Smooth manifolds | Mathematics | Theory of Computation | Applications of Mathematics | Engineering, general | Optimization | Linear connections | Space of paths | Local convexity | MATHEMATICS, APPLIED | smooth manifolds | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Studies | Theory | Manifolds | Convexity

space of paths | linear connections | Operations Research/Decision Theory | local convexity | Calculus of Variations and Optimal Control | Smooth manifolds | Mathematics | Theory of Computation | Applications of Mathematics | Engineering, general | Optimization | Linear connections | Space of paths | Local convexity | MATHEMATICS, APPLIED | smooth manifolds | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | Studies | Theory | Manifolds | Convexity

Journal Article

Journal of Integer Sequences, 03/2014, Volume 17, Issue 5

Journal Article

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