Linear Algebra and its Applications, ISSN 0024-3795, 12/2018, Volume 558, p. 236

We determine the unique hypertrees with maximum spectral radius among k-uniform non-hyper-caterpillars with m edges and diameter d for 4 ≤ d ≤ m -2, among...

Matrix | Vector space | Apexes | Linear algebra | Caterpillars | Graph theory | Number theory

Matrix | Vector space | Apexes | Linear algebra | Caterpillars | Graph theory | Number theory

Journal Article

TheScientificWorldJournal, ISSN 2356-6140, 2014, Volume 2014, pp. 637865 - 7

For a simple hypergraph H on n vertices, its Estrada index is defined as EE(H) = Sigma(n)(i=1) e(lambda i), where lambda(1), lambda(2), ... , lambda(n) are the...

PROTEINS | FOLDING DEGREE | UNICYCLIC GRAPHS | MULTIDISCIPLINARY SCIENCES | Humans | Mathematics | Models, Statistical | Linear systems | Trees (Graph theory) | Research | Mathematical research | Science | Graphs

PROTEINS | FOLDING DEGREE | UNICYCLIC GRAPHS | MULTIDISCIPLINARY SCIENCES | Humans | Mathematics | Models, Statistical | Linear systems | Trees (Graph theory) | Research | Mathematical research | Science | Graphs

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2019, Volume 261, pp. 186 - 192

A hypergraph is equitably k-colorable if its vertices can be partitioned into k sets/color classes in such a way that monochromatic edges are avoided and the...

Hypergraph | Feasible sequence | Linear hypertree | Equitable coloring | MATHEMATICS, APPLIED | GRAPHS | Analysis | Algorithms | Coloring | Apexes | Color | Graphs | Graph theory | Polynomials | Dynamic programming

Hypergraph | Feasible sequence | Linear hypertree | Equitable coloring | MATHEMATICS, APPLIED | GRAPHS | Analysis | Algorithms | Coloring | Apexes | Color | Graphs | Graph theory | Polynomials | Dynamic programming

Journal Article

The Computer Journal, ISSN 0010-4620, 5/2008, Volume 51, Issue 3, pp. 326 - 362

Besides the very successful concept of tree-width (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These...

Tree-width | Graph | MSO logic | Hypertree-width | Rank-width | Branch-width | Clique-width | Complexity | complexity | tree-width | branch-width | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | rank-width | COMPUTER SCIENCE, INFORMATION SYSTEMS | GRAPH MINORS | graph | hypertree-width | HYPERTREE DECOMPOSITIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | clique-width | PLANAR GRAPHS | MONADIC 2ND-ORDER LOGIC | DISJOINT PATHS | COMPUTER SCIENCE, THEORY & METHODS | LINEAR-TIME ALGORITHMS | Computer science | Graphs | Algorithms | Parameter optimization

Tree-width | Graph | MSO logic | Hypertree-width | Rank-width | Branch-width | Clique-width | Complexity | complexity | tree-width | branch-width | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | rank-width | COMPUTER SCIENCE, INFORMATION SYSTEMS | GRAPH MINORS | graph | hypertree-width | HYPERTREE DECOMPOSITIONS | COMPUTER SCIENCE, SOFTWARE ENGINEERING | clique-width | PLANAR GRAPHS | MONADIC 2ND-ORDER LOGIC | DISJOINT PATHS | COMPUTER SCIENCE, THEORY & METHODS | LINEAR-TIME ALGORITHMS | Computer science | Graphs | Algorithms | Parameter optimization

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 1998, Volume 82, Issue 1, pp. 43 - 77

The use of (generalized) tree structure in graphs is one of the main topics in the field of efficient graph algorithms. The well-known partial k-tree (resp....

Dominationm | Strongly chordal graph | Steiner tree | Hypertree | Disk hypergraph | Tree structure | Duality | Dually chordal graph | Maximum neighbourhood ordering | Location problem | Linear-time algorithm | Domination | PATH | hypertree | location problem | MATHEMATICS, APPLIED | dually chordal graph | domination | tree structure | STRONGLY CHORDAL GRAPHS | HYPERGRAPHS | strongly chordal graph | CENTERS | duality | LOCATION-PROBLEMS | linear-time algorithm | STEINER TREES | CONNECTED DOMINATION | disk hypergraph | MATRICES | maximum neighbourhood ordering

Dominationm | Strongly chordal graph | Steiner tree | Hypertree | Disk hypergraph | Tree structure | Duality | Dually chordal graph | Maximum neighbourhood ordering | Location problem | Linear-time algorithm | Domination | PATH | hypertree | location problem | MATHEMATICS, APPLIED | dually chordal graph | domination | tree structure | STRONGLY CHORDAL GRAPHS | HYPERGRAPHS | strongly chordal graph | CENTERS | duality | LOCATION-PROBLEMS | linear-time algorithm | STEINER TREES | CONNECTED DOMINATION | disk hypergraph | MATRICES | maximum neighbourhood ordering

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 04/2013, Volume 481, pp. 85 - 99

We show that the Satisfiability (SAT) problem for CNF formulas with β-acyclic hypergraphs can be solved in polynomial time by using a special type of...

Davis–Putnam resolution | Chordal bipartite graph | Acyclic hypergraph | Davis-Putnam resolution | BIPARTITE | HYPERGRAPHS | COMPLEXITY | CLIQUE-WIDTH | COMPUTER SCIENCE, THEORY & METHODS | LINEAR-TIME ALGORITHMS | HYPERTREE DECOMPOSITIONS | GRAPHS | Hardness | Trucking | Computer Science - Data Structures and Algorithms

Davis–Putnam resolution | Chordal bipartite graph | Acyclic hypergraph | Davis-Putnam resolution | BIPARTITE | HYPERGRAPHS | COMPLEXITY | CLIQUE-WIDTH | COMPUTER SCIENCE, THEORY & METHODS | LINEAR-TIME ALGORITHMS | HYPERTREE DECOMPOSITIONS | GRAPHS | Hardness | Trucking | Computer Science - Data Structures and Algorithms

Journal Article

Ars Combinatoria, ISSN 0381-7032, 07/2012, Volume 106, pp. 527 - 533

In this note it is shown that the number of cycles of a linear hypergraph is bounded below by its cyclomatic number.

Cyclomatic number | Hypertree | Linear hypergraph | linear hypergraph | MATHEMATICS | hypertree | cyclomatic number

Cyclomatic number | Hypertree | Linear hypergraph | linear hypergraph | MATHEMATICS | hypertree | cyclomatic number

Journal Article

European Journal of Operational Research, ISSN 0377-2217, 1998, Volume 108, Issue 3, pp. 696 - 709

One of the problems (mainly unsolved) in probabilistic logic is to consistently assign probabilities to logical formulas. In this paper we consider Horn...

Hypergraph | Integer programming | Probabilistic logic | Balanced matrix | Consistency | hypergraph | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | integer programming | probabilistic logic | balanced matrix | consistency | Linear programming | Probabilities | Research

Hypergraph | Integer programming | Probabilistic logic | Balanced matrix | Consistency | hypergraph | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | integer programming | probabilistic logic | balanced matrix | consistency | Linear programming | Probabilities | Research

Journal Article

Ars Combinatoria, ISSN 0381-7032, 01/2006, Volume 78, pp. 225 - 235

A hypergraph is a generalization of an ordinary graph, in which an edge is not limited to contain exactly two vertices, instead, it can contain an arbitrary...

Hypergraph | Pólya's Enumeration Theorem | Bipartite tree | Hypertree | Linear hypergraph | linear hypergraph | Polya's Enumeration Theorem | MATHEMATICS | hypertree | hypergraph | bipartite tree | ENUMERATION

Hypergraph | Pólya's Enumeration Theorem | Bipartite tree | Hypertree | Linear hypergraph | linear hypergraph | Polya's Enumeration Theorem | MATHEMATICS | hypertree | hypergraph | bipartite tree | ENUMERATION

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 1998, Volume 11, Issue 3, pp. 437 - 455

Recently in several papers, graphs with maximum neighborhood orderings were characterized and turned out to be algorithmically useful. This paper gives a...

Chordality of line graphs | Maximum neighborhood orderings | Helly property | Duality | Tree structure | Linear time recognition | Hypertrees | Disk hypergraphs | Graphs | Neighborhood hypergraphs | Hypergraphs | Chordal graphs | Doubly chordal graphs | Clique hypergraphs | MATHEMATICS, APPLIED | tree structure | chordal graphs | neighborhood hypergraphs | chordality of line graphs | ALGORITHMS | duality | hypertrees | strongly chordal graphs | maximum neighborhood orderings | bipartite incidence graphs | graphs | CLIQUE GRAPHS | hypergraphs | MATRICES | DOMINATION | disk hypergraphs | linear time recognition | ACYCLICITY | clique hypergraphs | doubly chordal graphs | DATABASE SCHEMES

Chordality of line graphs | Maximum neighborhood orderings | Helly property | Duality | Tree structure | Linear time recognition | Hypertrees | Disk hypergraphs | Graphs | Neighborhood hypergraphs | Hypergraphs | Chordal graphs | Doubly chordal graphs | Clique hypergraphs | MATHEMATICS, APPLIED | tree structure | chordal graphs | neighborhood hypergraphs | chordality of line graphs | ALGORITHMS | duality | hypertrees | strongly chordal graphs | maximum neighborhood orderings | bipartite incidence graphs | graphs | CLIQUE GRAPHS | hypergraphs | MATRICES | DOMINATION | disk hypergraphs | linear time recognition | ACYCLICITY | clique hypergraphs | doubly chordal graphs | DATABASE SCHEMES

Journal Article

Chinese Science Bulletin, ISSN 1001-6538, 2/2001, Volume 46, Issue 3, pp. 197 - 199

The explicit formula for (k+1)-uniform linear acyclic hypergraphs and the counting series for unlabeled (k + 1)-uniform linear acyclic hypergraphs are obtained.

linear hypergraph | hypertree | hypergraph | bipartite tree | Life Sciences, general | Chemistry/Food Science, general | Science, Humanities and Social Sciences, multidisciplinary | Pólya’s Enumeration Theorem | Earth Sciences, general | Physics, general | Engineering, general | Hypergraph | Pólya's Enumeration Theorem | Bipartite tree | Hypertree | Linear hypergraph | Polya's Enumeration Theorem | MULTIDISCIPLINARY SCIENCES

linear hypergraph | hypertree | hypergraph | bipartite tree | Life Sciences, general | Chemistry/Food Science, general | Science, Humanities and Social Sciences, multidisciplinary | Pólya’s Enumeration Theorem | Earth Sciences, general | Physics, general | Engineering, general | Hypergraph | Pólya's Enumeration Theorem | Bipartite tree | Hypertree | Linear hypergraph | Polya's Enumeration Theorem | MULTIDISCIPLINARY SCIENCES

Journal Article

Linear Algebra and its Applications, ISSN 0024-3795, 09/2017, Volume 529, p. 271

We determine the unique hypergraphs with minimum distance Laplacian spectral radius among connected k-uniform hypergraphs and k-uniform hypertrees,...

Matrix | Linear algebra | Graph theory | Spectra | Laplace transforms | Eigen values

Matrix | Linear algebra | Graph theory | Spectra | Laplace transforms | Eigen values

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 05/2013, Volume 161, Issue 7-8, pp. 1162 - 1167

The hierarchical product of graphs was introduced very recently by L. Barriére et al. in [L. Barriére, F. Comellas, C. Dafló and M. A. Fiol, On the spectra of...

Edge Szeged index | Revised Szeged index | Szeged index | Hierarchical product | DISTANCE-BALANCED GRAPHS | MATHEMATICS, APPLIED | Graphs | Mathematical analysis | Linear algebra | Spectral lines

Edge Szeged index | Revised Szeged index | Szeged index | Hierarchical product | DISTANCE-BALANCED GRAPHS | MATHEMATICS, APPLIED | Graphs | Mathematical analysis | Linear algebra | Spectral lines

Journal Article

Linear Algebra and its Applications, ISSN 0024-3795, 08/2017, Volume 527, p. 32

We prove a result concerning the behavior of the spectral radius of a hypergraph under relocations of edges. We determine the unique hypergraphs with maximum...

Matrix | Graphs | Spectra | Graph theory | Linear equations | Eigen values

Matrix | Graphs | Spectra | Graph theory | Linear equations | Eigen values

Journal Article

2008 42nd Asilomar Conference on Signals, Systems and Computers, ISSN 1058-6393, 10/2008, pp. 1805 - 1809

In this work a novel approach to the multiple constant multiplication problem, i.e., finding a realization of a number of constant multiplications by using...

Steiner trees | Energy consumption | Costs | NP-hard problem | Search methods | Hydrogen | Integer linear programming | Finite impulse response filter | Hardware | Delay

Steiner trees | Energy consumption | Costs | NP-hard problem | Search methods | Hydrogen | Integer linear programming | Finite impulse response filter | Hardware | Delay

Conference Proceeding

Theoretical Computer Science, ISSN 0304-3975, 2008, Volume 399, Issue 3, pp. 236 - 245

Graph searching encompasses a wide variety of combinatorial problems related to the problem of capturing a fugitive residing in a graph using the minimum...

Pursuit evasion in graphs | Graph searching | Fugitive search games | Cops and robbers games | MOBILE INTRUDER | NUMBER | VERTEX SEPARATION | MONOTONICITY | POLYGONAL REGION | DOMINATION SEARCH | COPS | graph searching | BRIDGED GRAPHS | cops and robbers games | fugitive search games | pursuit evasion in graphs | LINEAR-WIDTH | PURSUIT GAME | COMPUTER SCIENCE, THEORY & METHODS

Pursuit evasion in graphs | Graph searching | Fugitive search games | Cops and robbers games | MOBILE INTRUDER | NUMBER | VERTEX SEPARATION | MONOTONICITY | POLYGONAL REGION | DOMINATION SEARCH | COPS | graph searching | BRIDGED GRAPHS | cops and robbers games | fugitive search games | pursuit evasion in graphs | LINEAR-WIDTH | PURSUIT GAME | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Computational Intelligence and Neuroscience, ISSN 1687-5265, 2018, Volume 2018, pp. 2082875 - 9

As a tool of qualitative representation, conditional preference network (CP-net) has recently become a hot research topic in the field of artificial...

DECOMPOSITION | MODELS | CP-NETS | NEUROSCIENCES | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Problems | Nets | Algorithms | Semantics | Feedback | Decision making | Run time (computers) | Arc cutting | Linear programming | Internet service providers | Preferences | Artificial intelligence

DECOMPOSITION | MODELS | CP-NETS | NEUROSCIENCES | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Problems | Nets | Algorithms | Semantics | Feedback | Decision making | Run time (computers) | Arc cutting | Linear programming | Internet service providers | Preferences | Artificial intelligence

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2000, Volume 98, Issue 3, pp. 191 - 207

For an undirected graph G the kth power G k of G is the graph with the same vertex set as G where two vertices are adjacent iff their distance is at most k in...

Perfect elimination ordering | Metric power | LexBFS-ordering | Distance-hereditary graphs | Diameter | Linear-time algorithm | distance-hereditary graphs | MATHEMATICS, APPLIED | diameter | perfect elimination ordering | PERFECT ELIMINATION | metric power | POWERS | linear-time algorithm

Perfect elimination ordering | Metric power | LexBFS-ordering | Distance-hereditary graphs | Diameter | Linear-time algorithm | distance-hereditary graphs | MATHEMATICS, APPLIED | diameter | perfect elimination ordering | PERFECT ELIMINATION | metric power | POWERS | linear-time algorithm

Journal Article

Distributed Computing, ISSN 0178-2770, 11/2007, Volume 20, Issue 4, pp. 253 - 266

The problem of verifying a Minimum Spanning Tree (MST) was introduced by Tarjan in a sequential setting. Given a graph and a tree that spans it, the algorithm...

Self stabilization | Computer Systems Organization and Communication Networks | Computer Hardware | Computer Science | Labeling schemes | Minimum spanning tree | Software Engineering/Programming and Operating Systems | Network algorithms | Graph property verification | Theory of Computation | Computer Communication Networks | Proof labeling schemes | minimum spanning tree | STABILIZATION | ALGORITHM | GRAPHS | LINEAR-TIME | proof labeling schemes | graph property verification | COMPUTER SCIENCE, THEORY & METHODS | labeling schemes | network algorithms | self stabilization | SHORTEST-PATH TREES | SENSITIVITY ANALYSIS | Algorithms

Self stabilization | Computer Systems Organization and Communication Networks | Computer Hardware | Computer Science | Labeling schemes | Minimum spanning tree | Software Engineering/Programming and Operating Systems | Network algorithms | Graph property verification | Theory of Computation | Computer Communication Networks | Proof labeling schemes | minimum spanning tree | STABILIZATION | ALGORITHM | GRAPHS | LINEAR-TIME | proof labeling schemes | graph property verification | COMPUTER SCIENCE, THEORY & METHODS | labeling schemes | network algorithms | self stabilization | SHORTEST-PATH TREES | SENSITIVITY ANALYSIS | Algorithms

Journal Article

Annals of Operations Research, ISSN 0254-5330, 05/2018, pp. 1 - 7

One of the primary objectives of this paper is to generalize Hunter’s bound to m-regular hypergraphs. In particular, new upper and lower bounds for the...

Probability of union of events | Hunter’s bound | Lower and upper bound | Lower bounds | Linear programming | Graphs | Graph theory

Probability of union of events | Hunter’s bound | Lower and upper bound | Lower bounds | Linear programming | Graphs | Graph theory

Journal Article

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