Discrete Applied Mathematics, ISSN 0166-218X, 01/2016, Volume 199, pp. 16 - 29

Bichain graphs form a bipartite analog of split permutation graphs, also known as split graphs of Dilworth number 2...

Split permutation graph | Intersection graph | Universal graph | MATHEMATICS, APPLIED | CLIQUE-WIDTH | SUBGRAPHS | SPLIT GRAPHS

Split permutation graph | Intersection graph | Universal graph | MATHEMATICS, APPLIED | CLIQUE-WIDTH | SUBGRAPHS | SPLIT GRAPHS

Journal Article

2017, Graduate studies in mathematics, ISBN 9781470425562, Volume 184, x, 334 pages

Book

Discrete Applied Mathematics, ISSN 0166-218X, 2017, Volume 216, pp. 98 - 113

A rainbow path in an edge coloured graph is a path in which no two edges are coloured the same...

Split graph | Threshold graph | Rainbow colouring | Rainbow connectivity | Complexity | MATHEMATICS, APPLIED | CONNECTION NUMBER | HARDNESS

Split graph | Threshold graph | Rainbow colouring | Rainbow connectivity | Complexity | MATHEMATICS, APPLIED | CONNECTION NUMBER | HARDNESS

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

PLoS computational biology, ISSN 1553-7358, 2016, Volume 12, Issue 10, p. e1005151

Genetic variation at the Human Leucocyte Antigen (HLA) genes is associated with many autoimmune and infectious disease phenotypes, is an important element of...

CLASS-I | HIGH-RESOLUTION HLA | SUSCEPTIBILITY | BIOCHEMICAL RESEARCH METHODS | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Genetics, Population | Algorithms | Hemochromatosis Protein - genetics | Chromosome Mapping - methods | Humans | Reference Values | High-Throughput Nucleotide Sequencing - methods | Genome, Human - genetics | Histocompatibility antigens | HLA histocompatibility antigens | Genetic aspects | Nucleotide sequencing | Health aspects | Methods | DNA sequencing | Antigens | Accuracy | Infectious diseases | Laboratories | Funding | Genomics | Quality | Colleges & universities | Population | Genetics | Genomes | Life Sciences | Human health and pathology

CLASS-I | HIGH-RESOLUTION HLA | SUSCEPTIBILITY | BIOCHEMICAL RESEARCH METHODS | MATHEMATICAL & COMPUTATIONAL BIOLOGY | Genetics, Population | Algorithms | Hemochromatosis Protein - genetics | Chromosome Mapping - methods | Humans | Reference Values | High-Throughput Nucleotide Sequencing - methods | Genome, Human - genetics | Histocompatibility antigens | HLA histocompatibility antigens | Genetic aspects | Nucleotide sequencing | Health aspects | Methods | DNA sequencing | Antigens | Accuracy | Infectious diseases | Laboratories | Funding | Genomics | Quality | Colleges & universities | Population | Genetics | Genomes | Life Sciences | Human health and pathology

Journal Article

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...

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

SIAM journal on discrete mathematics, ISSN 0895-4801, 2014, Volume 28, Issue 3, pp. 1449 - 1466

Graph pebbling is a network optimization model for transporting discrete resources that are consumed in transit...

Split graphs | Class 0 | Pebbling number | Graph algorithms | Complexity | SPACE | complexity | MATHEMATICS, APPLIED | split graphs | DIAMETER 2 GRAPHS | class 0 | pebbling number | graph algorithms | Consumption | Algorithms | Orange peel | Graphs | Mathematical models | Polynomials | Transporting | Optimization

Split graphs | Class 0 | Pebbling number | Graph algorithms | Complexity | SPACE | complexity | MATHEMATICS, APPLIED | split graphs | DIAMETER 2 GRAPHS | class 0 | pebbling number | graph algorithms | Consumption | Algorithms | Orange peel | Graphs | Mathematical models | Polynomials | Transporting | Optimization

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 5/2015, Volume 31, Issue 3, pp. 713 - 727

In this paper, we introduce and study a new coloring problem of a graph called the dominated coloring...

Split graphs | Star-free graphs | Total domination | Algorithms | Triangle-free graphs | Dominated coloring | 05C85 | Mathematics | Engineering Design | Combinatorics | 05C15 | MATHEMATICS | TREES | Studies | Graphs | Color | Coloring | Equivalence | Texts | Polynomials | Recognition | Combinatorial analysis | Data Structures and Algorithms | Computer Science | Discrete Mathematics | Computational Complexity

Split graphs | Star-free graphs | Total domination | Algorithms | Triangle-free graphs | Dominated coloring | 05C85 | Mathematics | Engineering Design | Combinatorics | 05C15 | MATHEMATICS | TREES | Studies | Graphs | Color | Coloring | Equivalence | Texts | Polynomials | Recognition | Combinatorial analysis | Data Structures and Algorithms | Computer Science | Discrete Mathematics | Computational Complexity

Journal Article

Networks, ISSN 0028-3045, 07/2014, Volume 63, Issue 4, pp. 277 - 285

.... This problem takes as input a graph G and an integer kv for every vertex v of G, and the objective is to find a vertex subset S of minimum cardinality such that every vertex v either belongs to S, or...

approximation algorithm | tree | cograph | polynomial time algorithm | split graph | vector connectivity | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RECOGNITION | THEOREM | ALGORITHM | APPROXIMABILITY | Algorithms | Networks | Approximation | Mathematical analysis | Graphs | Polynomials | Boundaries | Vectors (mathematics) | Hardness

approximation algorithm | tree | cograph | polynomial time algorithm | split graph | vector connectivity | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | RECOGNITION | THEOREM | ALGORITHM | APPROXIMABILITY | Algorithms | Networks | Approximation | Mathematical analysis | Graphs | Polynomials | Boundaries | Vectors (mathematics) | Hardness

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 10/2016, Volume 211, pp. 30 - 39

A graph is H-free if it has no induced subgraph isomorphic to H. We continue a study into the boundedness of clique-width of subclasses of perfect graphs...

Split graph | Forbidden induced subgraph | Hereditary graph class | Perfect graph | Clique-width | MATHEMATICS, APPLIED | CO-GEM-FREE | (P-5,GEM)-FREE GRAPHS | FORBIDDEN SUBGRAPHS | TRIANGLE-FREE GRAPHS | BIPARTITE GRAPHS

Split graph | Forbidden induced subgraph | Hereditary graph class | Perfect graph | Clique-width | MATHEMATICS, APPLIED | CO-GEM-FREE | (P-5,GEM)-FREE GRAPHS | FORBIDDEN SUBGRAPHS | TRIANGLE-FREE GRAPHS | BIPARTITE GRAPHS

Journal Article

Discussiones Mathematicae Graph Theory, ISSN 1234-3099, 08/2016, Volume 36, Issue 3, pp. 723 - 741

We show that every 3-regular circle graph has at least two pairs of twin vertices...

split decomposition | regular graph | circle graph | Split decomposition | Circle graph | Regular graph | MATHEMATICS | DECOMPOSITION | RECOGNITION | Mathematics - Combinatorics

split decomposition | regular graph | circle graph | Split decomposition | Circle graph | Regular graph | MATHEMATICS | DECOMPOSITION | RECOGNITION | Mathematics - Combinatorics

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 5/2014, Volume 30, Issue 3, pp. 633 - 646

The class of split permutation graphs is the intersection of two important classes, the split graphs and permutation graphs...

Split graphs | Well-quasi-order | Mathematics | Engineering Design | Permutation graphs | Combinatorics | Clique-width | INDUCED SUBGRAPHS | MATHEMATICS | Graphs | Permutations | Extensibility | Thresholds | Intersections | Combinatorial analysis

Split graphs | Well-quasi-order | Mathematics | Engineering Design | Permutation graphs | Combinatorics | Clique-width | INDUCED SUBGRAPHS | MATHEMATICS | Graphs | Permutations | Extensibility | Thresholds | Intersections | Combinatorial analysis

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

Theoretical computer science, ISSN 0304-3975, 11/2015, Volume 607, pp. 60 - 67

...: Given a graph G, and an integer k as parameter, determine whether G can be modified into a split graph by contracting at most k edges...

Split graphs | FPT algorithm | Edge contraction | Incompressibility | Parameterized complexity | COMPUTER SCIENCE, THEORY & METHODS | Integers | Kernels | Graphs | Polynomials | Graph theory | Contraction | Complexity

Split graphs | FPT algorithm | Edge contraction | Incompressibility | Parameterized complexity | COMPUTER SCIENCE, THEORY & METHODS | Integers | Kernels | Graphs | Polynomials | Graph theory | Contraction | Complexity

Journal Article

The Electronic journal of combinatorics, ISSN 1077-8926, 03/2018, Volume 25, Issue 1

A graph is a split graph if its vertex set can be partitioned into a clique and a stable set...

Bipartite poset | Split graph | Bijection | Set cover | Bipartite graph | set cover | bijection | MATHEMATICS | MATHEMATICS, APPLIED | bipartite poset | ENUMERATION | bipartite graph | split graph

Bipartite poset | Split graph | Bijection | Set cover | Bipartite graph | set cover | bijection | MATHEMATICS | MATHEMATICS, APPLIED | bipartite poset | ENUMERATION | bipartite graph | split graph

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 03/2014, Volume 166, pp. 91 - 96

Matrix partition problems generalize a number of natural graph partition problems, and have been studied for several standard graph classes...

Split graphs | Forbidden subgraphs | Generalized graph colouring | Matrix partition | Minimal obstructions | MATHEMATICS, APPLIED | OBSTRUCTIONS | Lower bounds | Graphs | Partitions | Obstructions | Mathematical analysis | Standards

Split graphs | Forbidden subgraphs | Generalized graph colouring | Matrix partition | Minimal obstructions | MATHEMATICS, APPLIED | OBSTRUCTIONS | Lower bounds | Graphs | Partitions | Obstructions | Mathematical analysis | Standards

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...

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

Graphs and combinatorics, ISSN 0911-0119, 2012, Volume 29, Issue 5, pp. 1193 - 1206

Rado constructed a (simple) denumerable graph R with the positive integers as vertex set with the following edges...

Rado graph | H -colourable graph | k -colourable graph | ( k , l )-split graph | 05C63 | Mathematics | Engineering Design | Universal graph | Hom-property of graphs | Homogeneous graph | Combinatorics | Extension property of graphs | H-colourable graph | k-colourable graph | (k, l)-split graph | MATHEMATICS | Graph theory | Integers | Graphs | Construction | Combinatorial analysis

Rado graph | H -colourable graph | k -colourable graph | ( k , l )-split graph | 05C63 | Mathematics | Engineering Design | Universal graph | Hom-property of graphs | Homogeneous graph | Combinatorics | Extension property of graphs | H-colourable graph | k-colourable graph | (k, l)-split graph | MATHEMATICS | Graph theory | Integers | Graphs | Construction | Combinatorial analysis

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 216, pp. 47 - 66

We consider several graphs classes defined in terms of conditions on cliques and stable sets, including CIS, split, equistable, and other related classes...

Triangle condition | Equistable graph | CIS graph | General partition graph | Upper bound graph | Normal graph | Split graph | Clique | Stable set | Edge simplicial graph | MATHEMATICS, APPLIED | ALGORITHMS | COMPLEXITY | SETS

Triangle condition | Equistable graph | CIS graph | General partition graph | Upper bound graph | Normal graph | Split graph | Clique | Stable set | Edge simplicial graph | MATHEMATICS, APPLIED | ALGORITHMS | COMPLEXITY | SETS

Journal Article

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