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

.... Then G is called a square root of G2. Deciding whether a given graph has a square root is known to be NP-complete, even if the root is required to be a chordal graph or even a split graph...

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

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

.... Then G is called a square root of G2. Deciding whether a given graph has a square root is known to be NP-complete, even if the root is required to be a split graph...

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

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...

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

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

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

.... This result is obtained by developing a structural characterization of graphs that have a split square root...

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

Systematic Biology, ISSN 1063-5157, 2/2005, Volume 54, Issue 1, pp. 56 - 65

.... This optimization of branch lengths is generally expected to improve divergence time estimates calculated from splits graphs...

Datasets | Taxa | Biological taxonomies | Least squares | Phylogenetics | Evolution | Plants | Phylogeny | Estimated taxes | Goodness of fit | Biogeography | Reticulation | Hybridization | Split decomposition | Recent species radiation | split decomposition | DIVERSIFICATION | biogeography | SEQUENCE DATA | DECOMPOSITION | hybridization | recent species radiation | PHYLOGENETIC INFERENCE | CONCERTED EVOLUTION | MEDIAN NETWORKS | EVOLUTIONARY BIOLOGY | NUCLEAR RIBOSOMAL DNA | TREES | least squares | reticulation | CONSTRUCTION | PLANTS | Geography | New Zealand | Boraginaceae - genetics | Species Specificity | Least-Squares Analysis | Classification - methods | Models, Genetic | Ranunculus - genetics | Evolution, Molecular | Optimization techniques | Genetics | Flowers & plants

Datasets | Taxa | Biological taxonomies | Least squares | Phylogenetics | Evolution | Plants | Phylogeny | Estimated taxes | Goodness of fit | Biogeography | Reticulation | Hybridization | Split decomposition | Recent species radiation | split decomposition | DIVERSIFICATION | biogeography | SEQUENCE DATA | DECOMPOSITION | hybridization | recent species radiation | PHYLOGENETIC INFERENCE | CONCERTED EVOLUTION | MEDIAN NETWORKS | EVOLUTIONARY BIOLOGY | NUCLEAR RIBOSOMAL DNA | TREES | least squares | reticulation | CONSTRUCTION | PLANTS | Geography | New Zealand | Boraginaceae - genetics | Species Specificity | Least-Squares Analysis | Classification - methods | Models, Genetic | Ranunculus - genetics | Evolution, Molecular | Optimization techniques | Genetics | Flowers & plants

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 that are of distance 2...

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

Computational and mathematical methods in medicine, ISSN 1748-670X, 8/2013, Volume 2013, pp. 985819 - 16

.... The nonlocal total variation is taken as the L1-regularization functional and solved using Split Bregman iteration...

RECOVERY | REGULARIZATION | TOTAL VARIATION MINIMIZATION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | GRAPHS | Thorax - anatomy & histology | Heart - anatomy & histology | Algorithms | Brain - anatomy & histology | Humans | Image Interpretation, Computer-Assisted - methods | Magnetic Resonance Imaging - statistics & numerical data | Signal-To-Noise Ratio | Computational Biology | Least-Squares Analysis | Arteries - anatomy & histology | Data Compression - statistics & numerical data

RECOVERY | REGULARIZATION | TOTAL VARIATION MINIMIZATION | MATHEMATICAL & COMPUTATIONAL BIOLOGY | GRAPHS | Thorax - anatomy & histology | Heart - anatomy & histology | Algorithms | Brain - anatomy & histology | Humans | Image Interpretation, Computer-Assisted - methods | Magnetic Resonance Imaging - statistics & numerical data | Signal-To-Noise Ratio | Computational Biology | Least-Squares Analysis | Arteries - anatomy & histology | Data Compression - statistics & numerical data

Journal Article

Information Processing Letters, ISSN 0020-0190, 01/2011, Volume 111, Issue 3, pp. 120 - 123

... [Recognizing powers of proper interval, split and chordal graphs, SIAM J. Discrete Math. 18 (2004) 83–102] proved that recognizing squares of split graphs is an NP-complete problem...

Squares of split graphs | Graph algorithms | Graph powers | Good characterizations | COMPUTER SCIENCE, INFORMATION SYSTEMS | POWERS | Algorithms | Chemical properties | Intervals | Graphs

Squares of split graphs | Graph algorithms | Graph powers | Good characterizations | COMPUTER SCIENCE, INFORMATION SYSTEMS | POWERS | Algorithms | Chemical properties | Intervals | Graphs

Journal Article

Pacific Journal of Mathematics, ISSN 0030-8730, 2015, Volume 278, Issue 2, pp. 463 - 478

We give a technical result that implies a straightforward necessary and sufficient condition for a graph of groups with virtually cyclic edge groups to be one-ended...

Ends of groups | Groups acting on trees | Bass-Serre theory | Group theory | Square complexes | group theory | ends of groups | MATHEMATICS | groups acting on trees | DECOMPOSITIONS | square complexes | ACCESSIBILITY

Ends of groups | Groups acting on trees | Bass-Serre theory | Group theory | Square complexes | group theory | ends of groups | MATHEMATICS | groups acting on trees | DECOMPOSITIONS | square complexes | ACCESSIBILITY

Journal Article

International Journal of Pure and Applied Mathematics, ISSN 1311-8080, 2018, Volume 118, Issue 10, pp. 407 - 413

Journal Article

12.
Full Text
Polynomial time recognition of squares of ptolemaic graphs and 3-sun-free split graphs

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2014, Volume 8747, pp. 360 - 371

Conference Proceeding

2011, Encyclopedia of mathematics and its applications, ISBN 9780521461931, Volume 139., viii, 197

.... In many cases, solving such systems may depend more on the distribution of non-zero coefficients than on their values, so graph theory is also useful...

Geometry | Matrices | Graphic methods | Graph theory

Geometry | Matrices | Graphic methods | Graph theory

Book

Molecular Biology and Evolution, ISSN 0737-4038, 2/2007, Volume 24, Issue 2, pp. 532 - 538

We present QNet, a method for constructing split networks from weighted quartet trees...

Phylogenetic network | Quartet | SplitsTree | Phylogenetic tree | Neighbor-Net | Split network | phylogenetic tree | EVOLUTIONARY | BIOCHEMISTRY & MOLECULAR BIOLOGY | phylogenetic network | GRAPHS | split network | EVOLUTIONARY BIOLOGY | TREES | DNA | GENETICS & HEREDITY | quartet | Algorithms | Least-Squares Analysis | Salmonella - genetics | Models, Genetic | Software | Models, Statistical | Phylogeny | Data collection | Genetics | Taxonomy

Phylogenetic network | Quartet | SplitsTree | Phylogenetic tree | Neighbor-Net | Split network | phylogenetic tree | EVOLUTIONARY | BIOCHEMISTRY & MOLECULAR BIOLOGY | phylogenetic network | GRAPHS | split network | EVOLUTIONARY BIOLOGY | TREES | DNA | GENETICS & HEREDITY | quartet | Algorithms | Least-Squares Analysis | Salmonella - genetics | Models, Genetic | Software | Models, Statistical | Phylogeny | Data collection | Genetics | Taxonomy

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 07/2004, Volume 18, Issue 1, pp. 83 - 102

.... On the other hand, we show the NP-completeness of recognizing squares of chordal graphs, recognizing squares of split graphs, and recognizing chordal graphs...

Split graphs | Graph algorithms | Proper interval graphs | Graph powers | Chordal graphs | Graph roots | MATHEMATICS, APPLIED | proper interval graphs | SQUARE | split graphs | chordal graphs | graph roots | graph powers | ROOTS | TREE | CIRCULAR-ARC GRAPHS | ALGORITHMS | graph algorithms

Split graphs | Graph algorithms | Proper interval graphs | Graph powers | Chordal graphs | Graph roots | MATHEMATICS, APPLIED | proper interval graphs | SQUARE | split graphs | chordal graphs | graph roots | graph powers | ROOTS | TREE | CIRCULAR-ARC GRAPHS | ALGORITHMS | graph algorithms

Journal Article

7th Cologne-Twente Workshop on Graphs and Combinatorial Optimization, CTW 2008, 2008, pp. 123 - 126

Conference Proceeding

Random structures & algorithms, ISSN 1098-2418, 2019, Volume 55, Issue 2, pp. 271 - 289

We show the existence of rainbow perfect matchings in μn‐bounded edge colorings of Dirac bipartite graphs, for a sufficiently small μ > 0...

minimum degree | rainbow subgraphs | perfect matching | HAMILTON CYCLES | EXISTENCE | MATHEMATICS, APPLIED | BOLLOBAS | LOVASZ LOCAL LEMMA | CONJECTURE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | PLACEMENT | ELDRIDGE | LATIN SQUARES | Graphs | Graph theory | Graph coloring | Computer science | Grafs, Teoria de | Matemàtica | Informàtica | Teoria de grafs | Matemàtiques i estadística | Matemàtica discreta | Mathematics | Bipartite graphs | Àrees temàtiques de la UPC

minimum degree | rainbow subgraphs | perfect matching | HAMILTON CYCLES | EXISTENCE | MATHEMATICS, APPLIED | BOLLOBAS | LOVASZ LOCAL LEMMA | CONJECTURE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | PLACEMENT | ELDRIDGE | LATIN SQUARES | Graphs | Graph theory | Graph coloring | Computer science | Grafs, Teoria de | Matemàtica | Informàtica | Teoria de grafs | Matemàtiques i estadística | Matemàtica discreta | Mathematics | Bipartite graphs | Àrees temàtiques de la UPC

Journal Article

IEEE Transactions on Pattern Analysis and Machine Intelligence, ISSN 0162-8828, 08/1993, Volume 15, Issue 8, pp. 808 - 815

The performance of the classic split-and-merge segmentation algorithm is severely hampered by its rigid split-and-merge processes, which are insensitive to the image semantics...

Computer science | Image segmentation | Image edge detection | Councils | Merging | Approximation algorithms | Data structures | Computational efficiency | Machine intelligence | region adjacency graph | split-and-merge | segmentation | Algorithms | edge detection | piecewise least-square approximation | SPLIT-AND-MERGE | PIECEWISE LEAST-SQUARE APPROXIMATION | REGION ADJACENCY GRAPH | SEGMENTATION | ALGORITHMS | EDGE DETECTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Research | Machine vision | Image processing

Computer science | Image segmentation | Image edge detection | Councils | Merging | Approximation algorithms | Data structures | Computational efficiency | Machine intelligence | region adjacency graph | split-and-merge | segmentation | Algorithms | edge detection | piecewise least-square approximation | SPLIT-AND-MERGE | PIECEWISE LEAST-SQUARE APPROXIMATION | REGION ADJACENCY GRAPH | SEGMENTATION | ALGORITHMS | EDGE DETECTION | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Research | Machine vision | Image processing

Journal Article

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2017, Volume 10520, pp. 234 - 248

Conference Proceeding

Signal Processing, ISSN 0165-1684, 10/2014, Volume 103, pp. 103 - 113

.... The nonlocal total variation and wavelet sparsity are taken as the hybrid L1-regularization functional and solving it using a Split Bregman algorithm...

Split Bregman algorithm | Nonlocal total variation | MR image reconstruction | Compressed sensing | NONLOCAL REGULARIZATION | RECOVERY | IMAGE | ALGORITHMS | TOTAL VARIATION MINIMIZATION | GRAPHS | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Magnetic resonance imaging | Cells | Medical imaging equipment | Wavelet | Reconstruction | Fittings | Least squares method | Compressed | Regularization | Image reconstruction

Split Bregman algorithm | Nonlocal total variation | MR image reconstruction | Compressed sensing | NONLOCAL REGULARIZATION | RECOVERY | IMAGE | ALGORITHMS | TOTAL VARIATION MINIMIZATION | GRAPHS | ENGINEERING, ELECTRICAL & ELECTRONIC | Algorithms | Magnetic resonance imaging | Cells | Medical imaging equipment | Wavelet | Reconstruction | Fittings | Least squares method | Compressed | Regularization | Image reconstruction

Journal Article

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