Discrete Mathematics, ISSN 0012-365X, 05/2020, Volume 343, Issue 5, p. 111769

For a graph G=(V,E) and positive integer p, the exact distance-pgraph G[♮p] is the graph with vertex set...

Chordal graph | Tree-width | Adjacent-cliques graph | Isometric subgraph | Exact distance graph | Genus | MATHEMATICS | POWERS

Chordal graph | Tree-width | Adjacent-cliques graph | Isometric subgraph | Exact distance graph | Genus | MATHEMATICS | POWERS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 2018, Volume 243, pp. 239 - 247

In this work we investigate the chordality of squares and line graph squares of graphs...

Chordal graph | Graph square | Line graph | MATHEMATICS, APPLIED | POWERS

Chordal graph | Graph square | Line graph | MATHEMATICS, APPLIED | POWERS

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 05/2019, Volume 39, Issue 2, pp. 365 - 374

Several recent papers have investigated unichord-free graphs—the graphs in which no cycle has a unique chord...

05C75 | unichord-free graph | strongly chordal graph | MATHEMATICS

05C75 | unichord-free graph | strongly chordal graph | MATHEMATICS

Journal Article

Algorithmica, ISSN 0178-4617, 8/2014, Volume 69, Issue 4, pp. 884 - 905

A spanning tree T of a graph G is called a tree t-spanner of G if the distance between every pair of vertices in T is at most t times their distance in G...

Minimum max-stretch spanning tree problem | Balanced separators | Theory of Computation | Robertson-Seymour’s tree-decomposition | Generalized chordal graphs | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | Tree t -spanner problem | Approximation algorithms | Graph algorithms | Algorithm Analysis and Problem Complexity | Tree t-spanner problem | Robertson-Seymour's tree-decomposition | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | COMPLEXITY | LENGTH | Computer science

Minimum max-stretch spanning tree problem | Balanced separators | Theory of Computation | Robertson-Seymour’s tree-decomposition | Generalized chordal graphs | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | Tree t -spanner problem | Approximation algorithms | Graph algorithms | Algorithm Analysis and Problem Complexity | Tree t-spanner problem | Robertson-Seymour's tree-decomposition | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | COMPLEXITY | LENGTH | Computer science

Journal Article

Linear algebra and its applications, ISSN 0024-3795, 2019

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 06/2014, Volume 540-541, Issue 1, pp. 89 - 102

In this paper, we consider the selective graph coloring problem. Given an integer k≥1 and a graph G=(V,E) with a partition V1...

Split graphs | PTAS | Complete q-partite graphs | Approximation algorithms | Scheduling | Clustering | Computational complexity | Bipartite graphs | CHORDAL GRAPHS | COMPUTER SCIENCE, THEORY & METHODS | Integers | Graphs | Partitions | Graph coloring | Complexity | Computer Science

Split graphs | PTAS | Complete q-partite graphs | Approximation algorithms | Scheduling | Clustering | Computational complexity | Bipartite graphs | CHORDAL GRAPHS | COMPUTER SCIENCE, THEORY & METHODS | Integers | Graphs | Partitions | Graph coloring | Complexity | Computer Science

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 10/2018, Volume 745, pp. 75 - 86

.... The celebrated result of Lewis and Yannakakis gives a complete dichotomy of their complexity. It however has nothing to say about the case when the input graph is also special...

Vertex deletion problem | Chordal graph | Split graph | (Unit) interval graph | Hereditary property | Maximum (induced) subgraph | FIXED-PARAMETER | COMPUTER SCIENCE, THEORY & METHODS | SUBGRAPHS | HEREDITARY PROPERTIES | SPLIT | BIPARTITE GRAPHS | Information science | Algorithms

Vertex deletion problem | Chordal graph | Split graph | (Unit) interval graph | Hereditary property | Maximum (induced) subgraph | FIXED-PARAMETER | COMPUTER SCIENCE, THEORY & METHODS | SUBGRAPHS | HEREDITARY PROPERTIES | SPLIT | BIPARTITE GRAPHS | Information science | Algorithms

Journal Article

Journal of Combinatorial Optimization, ISSN 1382-6905, 1/2014, Volume 27, Issue 1, pp. 132 - 143

A k-colouring of a graph G=(V,E) is a mapping c:V→{1,2,…,k} such that c(u)≠c(v) whenever uv is an edge...

Reconfigurations | Convex and Discrete Geometry | Operations Research/Decision Theory | Graph diameter | Graph colouring | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Combinatorics | Optimization | Chordal graphs | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Computer Science | Discrete Mathematics

Reconfigurations | Convex and Discrete Geometry | Operations Research/Decision Theory | Graph diameter | Graph colouring | Mathematics | Theory of Computation | Mathematical Modeling and Industrial Mathematics | Combinatorics | Optimization | Chordal graphs | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | Computer Science | Discrete Mathematics

Journal Article

Journal of Scheduling, ISSN 1094-6136, 02/2019, Volume 22, Issue 1, pp. 3 - 20

Inductive k-independent graphs generalize chordal graphs and have recently been advocated in the context of interference-avoiding wireless communication scheduling...

Interval graphs | NP-hard problems | Job interval selection | Independent set | Inductive k-independent graphs | Chordal graphs | Parameterized complexity | INTERVAL-GRAPHS | NUMBER | RECOGNITION | MULTIVARIATE ALGORITHMICS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | JOBS | ENGINEERING, MANUFACTURING

Interval graphs | NP-hard problems | Job interval selection | Independent set | Inductive k-independent graphs | Chordal graphs | Parameterized complexity | INTERVAL-GRAPHS | NUMBER | RECOGNITION | MULTIVARIATE ALGORITHMICS | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | JOBS | ENGINEERING, MANUFACTURING

Journal Article

The Annals of statistics, ISSN 0090-5364, 6/2007, Volume 35, Issue 3, pp. 1278 - 1323

When considering a graphical Gaussian model $\scr{N}_{G}$ Markov with respect to a decomposable graph G, the parameter space of interest for the precision parameter is the cone $P_{G...

Hasse diagrams | Induced subgraphs | Mathematical independent variables | Markov models | Laplace transformation | Separators | Children | Parametric models | Vertices | Jacobians | Wisharts for Decomposable Graphs | Graphical models | Homogeneous cones | Covariance selection models | Hyper Markov | Inverse wishart | Natural exponential families | Triangulated graphs | Hyper Wishart and hyper inverse Wishart | Conjugate priors | Perfect order | Chordal graphs | PRIORS | chordal graphs | natural exponential families | ENRICHED CONJUGATE | conjugate priors | STATISTICS & PROBABILITY | hyper Markov | hyper Wishart and hyper inverse Wishart | perfect order | graphical models | homogeneous cones | covariance selection models | triangulated graphs | inverse Wishart | 62H99 | 62E15

Hasse diagrams | Induced subgraphs | Mathematical independent variables | Markov models | Laplace transformation | Separators | Children | Parametric models | Vertices | Jacobians | Wisharts for Decomposable Graphs | Graphical models | Homogeneous cones | Covariance selection models | Hyper Markov | Inverse wishart | Natural exponential families | Triangulated graphs | Hyper Wishart and hyper inverse Wishart | Conjugate priors | Perfect order | Chordal graphs | PRIORS | chordal graphs | natural exponential families | ENRICHED CONJUGATE | conjugate priors | STATISTICS & PROBABILITY | hyper Markov | hyper Wishart and hyper inverse Wishart | perfect order | graphical models | homogeneous cones | covariance selection models | triangulated graphs | inverse Wishart | 62H99 | 62E15

Journal Article

Information Processing Letters, ISSN 0020-0190, 02/2015, Volume 115, Issue 2, pp. 256 - 262

An efficient dominating set (or perfect code) in a graph is a set of vertices the closed neighborhoods of which partition the vertex set of the graph...

Efficient domination | Weighted efficient domination | AT-free graph | Graph algorithms | Dually chordal graph | PERFECT DOMINATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | INDEPENDENT SETS | Computer science | Algorithms | Minimum weight | Reduction | Partitions | Weight reduction | Data processing | Graphs | Complexity | Computer Science - Discrete Mathematics

Efficient domination | Weighted efficient domination | AT-free graph | Graph algorithms | Dually chordal graph | PERFECT DOMINATION | COMPUTER SCIENCE, INFORMATION SYSTEMS | INDEPENDENT SETS | Computer science | Algorithms | Minimum weight | Reduction | Partitions | Weight reduction | Data processing | Graphs | Complexity | Computer Science - Discrete Mathematics

Journal Article

Journal of Combinatorial Theory, Series A, ISSN 0097-3165, 04/2016, Volume 139, pp. 30 - 58

.... In this paper, we study when entrywise powers preserve positivity for matrices with structure of zeros encoded by graphs...

Matrices with structure of zeros | Entrywise positive maps | Positive semidefiniteness | Loewner ordering | Chordal graphs | Fractional Schur powers | MATHEMATICS | HADAMARD POWERS | COMPLETIONS | POSITIVE SEMIDEFINITE MATRICES | DEFINITE MATRICES

Matrices with structure of zeros | Entrywise positive maps | Positive semidefiniteness | Loewner ordering | Chordal graphs | Fractional Schur powers | MATHEMATICS | HADAMARD POWERS | COMPLETIONS | POSITIVE SEMIDEFINITE MATRICES | DEFINITE MATRICES

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 01/2017, Volume 122, pp. 417 - 427

Chen et al. (1998) proved that every 18-tough chordal graph has a Hamilton cycle...

Chordal graph | Hamilton cycle | Toughness | Hamilton-connected graph | MATHEMATICS

Chordal graph | Hamilton cycle | Toughness | Hamilton-connected graph | MATHEMATICS

Journal Article

Journal of algebraic combinatorics, ISSN 1572-9192, 2017, Volume 47, Issue 1, pp. 17 - 38

Let G be a finite simple graph and I(G) denote the corresponding edge ideal. For all $$s \ge 1$$ s≥1 , we obtain upper bounds...

Castelnuovo–Mumford regularity | Induced matching number | Edge ideal | Convex and Discrete Geometry | Co-chordal cover number | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Bipartite graphs | MATHEMATICS | Castelnuovo-Mumford regularity | EDGE IDEALS | PROJECTIVE DIMENSION | MATCHINGS | ASYMPTOTIC-BEHAVIOR

Castelnuovo–Mumford regularity | Induced matching number | Edge ideal | Convex and Discrete Geometry | Co-chordal cover number | Mathematics | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Bipartite graphs | MATHEMATICS | Castelnuovo-Mumford regularity | EDGE IDEALS | PROJECTIVE DIMENSION | MATCHINGS | ASYMPTOTIC-BEHAVIOR

Journal Article

Journal of combinatorial optimization, ISSN 1573-2886, 2012, Volume 26, Issue 3, pp. 608 - 619

Given real numbers b≥a>0, an (a,b)-Roman dominating function of a graph G=(V,E) is a function f:V→{0,a,b} such that every vertex v with f...

Mathematics | Theory of Computation | Optimization | Domination | Split graphs | Convex and Discrete Geometry | Operations Research/Decision Theory | Roman domination | Mathematical Modeling and Industrial Mathematics | Strongly chordal graphs | Combinatorics | Bipartite graphs | Chordal graphs | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EMPIRE | STRATEGY | INDEPENDENT DOMINATION | Algorithms

Mathematics | Theory of Computation | Optimization | Domination | Split graphs | Convex and Discrete Geometry | Operations Research/Decision Theory | Roman domination | Mathematical Modeling and Industrial Mathematics | Strongly chordal graphs | Combinatorics | Bipartite graphs | Chordal graphs | MATHEMATICS, APPLIED | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | EMPIRE | STRATEGY | INDEPENDENT DOMINATION | Algorithms

Journal Article

ARS COMBINATORIA, ISSN 0381-7032, 04/2015, Volume 120, pp. 259 - 274

A graph is closed when its vertices have a labeling by [n] with a certain property first discovered in the study of binomial edge ideals...

MATHEMATICS | binomial edge ideal | chordal graph | closed graph

MATHEMATICS | binomial edge ideal | chordal graph | closed graph

Journal Article

Discrete Mathematics, ISSN 0012-365X, 2010, Volume 310, Issue 23, pp. 3398 - 3403

We prove a decomposition theorem for the class G of { P 2 ∪ P 3 , C 4 } -free graphs. This theorem enables us to show...

Maximal cliques | [formula omitted]-free graphs | Chromatic number | Chordal graphs | free graphs | MATHEMATICS | SETS | C-4-free graphs | Graphs | Theorems | Decomposition | Mathematical analysis | Images

Maximal cliques | [formula omitted]-free graphs | Chromatic number | Chordal graphs | free graphs | MATHEMATICS | SETS | C-4-free graphs | Graphs | Theorems | Decomposition | Mathematical analysis | Images

Journal Article

TURKISH JOURNAL OF MATHEMATICS, ISSN 1300-0098, 2019, Volume 43, Issue 5, pp. 2405 - 2414

The independence complex of a chordal graph is known to be shellable which is equivalent to the fact that cover ideal of a chordal graph has linear quotients...

MATHEMATICS | Chordal graph | shellable | linear quotients | cover ideal | Betti numbers

MATHEMATICS | Chordal graph | shellable | linear quotients | cover ideal | Betti numbers

Journal Article

ACM Transactions on Algorithms (TALG), ISSN 1549-6325, 01/2018, Volume 14, Issue 1, pp. 1 - 30

In the M aximum W eight I ndependent S et problem, the input is a graph G , every vertex has a non-negative integer weight, and the task is to find a set S of pairwise nonadjacent vertices, maximizing...

(quasi)polynomial-time algorithms | P 6 -free graphs | efficient domination | Independence | MAXIMUM WEIGHT | MATHEMATICS, APPLIED | (quasi) polynomial-time algorithms | P-5-FREE GRAPHS | SEPARATORS | P-6-free graphs | POLYNOMIAL ALGORITHM | STABLE SET PROBLEM | CHORDAL GRAPHS | P-6 | COMPUTER SCIENCE, THEORY & METHODS

(quasi)polynomial-time algorithms | P 6 -free graphs | efficient domination | Independence | MAXIMUM WEIGHT | MATHEMATICS, APPLIED | (quasi) polynomial-time algorithms | P-5-FREE GRAPHS | SEPARATORS | P-6-free graphs | POLYNOMIAL ALGORITHM | STABLE SET PROBLEM | CHORDAL GRAPHS | P-6 | COMPUTER SCIENCE, THEORY & METHODS

Journal Article

Electronic Journal of Combinatorics, ISSN 1077-8926, 09/2016, Volume 23, Issue 3

Let G be a graph with the usual shortest-path metric. A graph is delta-hyperbolic if for every geodesic triangle T, any side of T is contained in a delta-neighborhood of the union of the other two sides...

Geodesic | Infinite graph | Gromov hyperbolic | Chordal | MATHEMATICS | MATHEMATICS, APPLIED | geodesic | chordal | GROMOV-HYPERBOLICITY | CONSTANT

Geodesic | Infinite graph | Gromov hyperbolic | Chordal | MATHEMATICS | MATHEMATICS, APPLIED | geodesic | chordal | GROMOV-HYPERBOLICITY | CONSTANT

Journal Article

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