Discrete Mathematics, ISSN 0012-365X, 04/2012, Volume 312, Issue 7, pp. 1314 - 1325

We generalize the class of split graphs to the directed case and show that these split digraphs can be identified from their degree sequences. The first degree...

Split graph | Directed graph | Degree sequence | GRAPH | MATHEMATICS

Split graph | Directed graph | Degree sequence | GRAPH | MATHEMATICS

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 01/2017, Volume 216, pp. 609 - 617

We introduce new versions of chordal and split digraphs, and explore their similarity with the corresponding undirected notions.

Split digraph | Chordal digraph | Perfect digraph | Recognition algorithm | MATHEMATICS, APPLIED | RECOGNIZING INTERVAL-GRAPHS | RECOGNITION | ACYCLIC DIGRAPHS | TIME | ALGORITHMS

Split digraph | Chordal digraph | Perfect digraph | Recognition algorithm | MATHEMATICS, APPLIED | RECOGNIZING INTERVAL-GRAPHS | RECOGNITION | ACYCLIC DIGRAPHS | TIME | ALGORITHMS

Journal Article

Discrete Mathematics, ISSN 0012-365X, 05/2017, Volume 340, Issue 5, pp. 851 - 854

A path partition P of a digraph D is a set of disjoint paths which covers V(D). Let k be a positive integer. The k-norm of a path partition P of a digraph is...

Split digraph | Path partition | Linial's conjecture | k-partial coloring | MATHEMATICS | THEOREM | PATH PARTITION CONJECTURE | PROOF

Split digraph | Path partition | Linial's conjecture | k-partial coloring | MATHEMATICS | THEOREM | PATH PARTITION CONJECTURE | PROOF

Journal Article

Applicable Analysis and Discrete Mathematics, ISSN 1452-8630, 4/2019, Volume 13, Issue 1, pp. 224 - 239

Fault tolerance is especially important for interconnection networks, since the growing size of networks increases their vulnerability to component failures. A...

Integers | Sufficient conditions | Fault tolerance | Toughness | Mathematical theorems | Real numbers | Discrete mathematics | Kronecker product | Vertices | RANDIC INDEX | MATHEMATICS | digraphs | MATHEMATICS, APPLIED | k-multisplit graphs | Maximally edge-connected | SPLIT GRAPHS | super-edge-connected | the zeroth-order general Randic index | EDGE VULNERABILITY PARAMETERS

Integers | Sufficient conditions | Fault tolerance | Toughness | Mathematical theorems | Real numbers | Discrete mathematics | Kronecker product | Vertices | RANDIC INDEX | MATHEMATICS | digraphs | MATHEMATICS, APPLIED | k-multisplit graphs | Maximally edge-connected | SPLIT GRAPHS | super-edge-connected | the zeroth-order general Randic index | EDGE VULNERABILITY PARAMETERS

Journal Article

ACM Transactions on Algorithms (TALG), ISSN 1549-6325, 06/2018, Volume 14, Issue 2, pp. 1 - 26

Motivated by applications in cancer genomics and following the work of Hajirasouliha and Raphael (WABI 2014), Hujdurović et al. (IEEE TCBB, 2018) introduced...

min-max theorem | minimum conflict-free row split problem | Perfect phylogeny | approximation algorithm | chain partition | APX-hardness | branching | acyclic digraph | Dilworth's theorem | Branching | Acyclic digraph | Minimum conflict-free row split problem | Approximation algorithm | Min-max theorem | Chain partition

min-max theorem | minimum conflict-free row split problem | Perfect phylogeny | approximation algorithm | chain partition | APX-hardness | branching | acyclic digraph | Dilworth's theorem | Branching | Acyclic digraph | Minimum conflict-free row split problem | Approximation algorithm | Min-max theorem | Chain partition

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 10/2018, Volume 247, pp. 122 - 126

P. Hell and C. Hernández-Cruz recently defined new directed graph analogs of the traditional concepts of chordal and split graphs. This paper will provide...

Chordal graph | Split graph | Clique tree | Strict split digraph | Strict chordal digraph | MATHEMATICS, APPLIED

Chordal graph | Split graph | Clique tree | Strict split digraph | Strict chordal digraph | MATHEMATICS, APPLIED

Journal Article

Discrete Mathematics, ISSN 0012-365X, 05/2017, Volume 340, Issue 5, pp. 851 - 854

A path partition P of a digraph D is a set of disjoint paths which covers V(D). Let k be a positive integer. The k-norm of a path partition P of a digraph is...

Split digraph | Path partition | [formula omitted]-partial coloring | Linial’s conjecture

Split digraph | Path partition | [formula omitted]-partial coloring | Linial’s conjecture

Journal Article

8.
Full Text
Hoffman polynomials of nonnegative irreducible matrices and strongly connected digraphs

Linear Algebra and Its Applications, ISSN 0024-3795, 2006, Volume 414, Issue 1, pp. 138 - 171

For a nonnegative n × n matrix A, we find that there is a polynomial f ( x ) ∈ R [ x ] such that f( A) is a positive matrix of rank one if and only if A is...

Perron eigenvalue | Perron eigenvector | Tensor product | Perron pair | Amalgamation | Elementary equivalence | Split | Matrix equation | Harmonic digraph | perron pair | harmonic digraph | FIXED LENGTH | MATHEMATICS, APPLIED | IDENTITIES | TENSOR-PRODUCTS | REGULAR GRAPHS | ELEMENTARY DIVISORS | J-I | matrix equation | UNIQUE PATHS | perron eigenvector | tensor product | elementary equivalence | split | DIRECTED GRAPH | perron eigenvalue | amalgamation | SPECTRA | MOORE GRAPHS

Perron eigenvalue | Perron eigenvector | Tensor product | Perron pair | Amalgamation | Elementary equivalence | Split | Matrix equation | Harmonic digraph | perron pair | harmonic digraph | FIXED LENGTH | MATHEMATICS, APPLIED | IDENTITIES | TENSOR-PRODUCTS | REGULAR GRAPHS | ELEMENTARY DIVISORS | J-I | matrix equation | UNIQUE PATHS | perron eigenvector | tensor product | elementary equivalence | split | DIRECTED GRAPH | perron eigenvalue | amalgamation | SPECTRA | MOORE GRAPHS

Journal Article

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

Book

ALGORITHMICA, ISSN 0178-4617, 03/2020, Volume 82, Issue 3, pp. 589 - 615

We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a...

COMPUTER SCIENCE, SOFTWARE ENGINEERING | Permutations | MATHEMATICS, APPLIED | Inversions | Split trees | Random trees | Cumulants

COMPUTER SCIENCE, SOFTWARE ENGINEERING | Permutations | MATHEMATICS, APPLIED | Inversions | Split trees | Random trees | Cumulants

Journal Article

ACM TRANSACTIONS ON ALGORITHMS, ISSN 1549-6325, 06/2018, Volume 14, Issue 2

Motivated by applications in cancer genomics and following the work of Hajirasouliha and Raphael (WABI 2014), Hujdurovic et al. (IEEE TCBB, 2018) introduced...

MATHEMATICS, APPLIED | BIPARTITE | min-max theorem | minimum conflict-free row split problem | APPROXIMATION | Perfect phylogeny | chain partition | APX-hardness | ALGORITHMS | branching | Dilworth's theorem | GRAPHS | TREES | COMPLEXITY | approximation algorithm | COMPUTER SCIENCE, THEORY & METHODS | acyclic digraph

MATHEMATICS, APPLIED | BIPARTITE | min-max theorem | minimum conflict-free row split problem | APPROXIMATION | Perfect phylogeny | chain partition | APX-hardness | ALGORITHMS | branching | Dilworth's theorem | GRAPHS | TREES | COMPLEXITY | approximation algorithm | COMPUTER SCIENCE, THEORY & METHODS | acyclic digraph

Journal Article

Huagong Xuebao/CIESC Journal, ISSN 0438-1157, 12/2016, Volume 67, Issue 12, pp. 5098 - 5104

Journal Article

2020, Volume 82, Issue 3

We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a...

Permutations | Naturvetenskap | Inversions | Split trees | Mathematics | Natural Sciences | Matematik | Random trees | Cumulants

Permutations | Naturvetenskap | Inversions | Split trees | Mathematics | Natural Sciences | Matematik | Random trees | Cumulants

Publication

2020, Volume 82, Issue 3

We investigate the number of permutations that occur in random labellings of trees. This is a generalisation of the number of subpermutations occurring in a...

Data- och informationsvetenskap | Permutations | Inversions | Split trees | Mathematics | Computer and Information Sciences | Random trees | Naturvetenskap | Computer Sciences | Datavetenskap (datalogi) | Natural Sciences | Matematik | Sannolikhetsteori och statistik | Cumulants | Probability Theory and Statistics

Data- och informationsvetenskap | Permutations | Inversions | Split trees | Mathematics | Computer and Information Sciences | Random trees | Naturvetenskap | Computer Sciences | Datavetenskap (datalogi) | Natural Sciences | Matematik | Sannolikhetsteori och statistik | Cumulants | Probability Theory and Statistics

Publication

Ars Combinatoria, ISSN 0381-7032, 01/2010, Volume 94, pp. 25 - 32

The super (resp., edge-) connectivity of a connected graph is the minimum cardinality of a vertex-cut (resp., an edge-cut) whose removal does not isolate a...

Möbius cubes | Super connectivity | Locally twisted cubes | Connectivity | Hypercubes | Restricted connectivity | Cross cubes | Twisted cubes | SPLIT-STARS | restricted connectivity | SUPERCONNECTIVITY | Mobius cubes | super connectivity | hypercubes | DIGRAPHS | CONDITIONAL EDGE-CONNECTIVITY | twisted cubes | MATHEMATICS | cross cubes | locally twisted cubes | ALTERNATING GROUP GRAPHS

Möbius cubes | Super connectivity | Locally twisted cubes | Connectivity | Hypercubes | Restricted connectivity | Cross cubes | Twisted cubes | SPLIT-STARS | restricted connectivity | SUPERCONNECTIVITY | Mobius cubes | super connectivity | hypercubes | DIGRAPHS | CONDITIONAL EDGE-CONNECTIVITY | twisted cubes | MATHEMATICS | cross cubes | locally twisted cubes | ALTERNATING GROUP GRAPHS

Journal Article

UTILITAS MATHEMATICA, ISSN 0315-3681, 06/2017, Volume 103, pp. 237 - 243

The feedback number of a graph G is the minimum number of vertices whose removal from G results in an acyclic subgraph. Use f (AG(n)) to denote the feedback...

feedback vertex set | SPLIT-STARS | MATHEMATICS, APPLIED | NUMBERS | alternating group graphs | STATISTICS & PROBABILITY | cycles | acyclic subgraph | DIGRAPHS | feedback number

feedback vertex set | SPLIT-STARS | MATHEMATICS, APPLIED | NUMBERS | alternating group graphs | STATISTICS & PROBABILITY | cycles | acyclic subgraph | DIGRAPHS | feedback number

Journal Article

Computational Statistics and Data Analysis, ISSN 0167-9473, 2006, Volume 50, Issue 3, pp. 611 - 641

An ML estimation method is proposed for a recursive model of categorical variables which is too large to handle as a single model. The whole model is first...

Hyper-EM condition | D-split | Family condition | Junction tree of submodels | Node removability | Hyper-EM graph | Consistency of distribution | T-split | FIELDS | MAXIMUM-LIKELIHOOD | ACYCLIC DIGRAPHS | ALGORITHM | consistency of distribution | STATISTICS & PROBABILITY | MARKOV EQUIVALENCE | family condition | node removability | CONTINGENCY-TABLES | junction tree of submodels | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INDEPENDENCE | hyper-EM graph | SYSTEMS | hyper-EM condition | VARIABLES

Hyper-EM condition | D-split | Family condition | Junction tree of submodels | Node removability | Hyper-EM graph | Consistency of distribution | T-split | FIELDS | MAXIMUM-LIKELIHOOD | ACYCLIC DIGRAPHS | ALGORITHM | consistency of distribution | STATISTICS & PROBABILITY | MARKOV EQUIVALENCE | family condition | node removability | CONTINGENCY-TABLES | junction tree of submodels | COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS | INDEPENDENCE | hyper-EM graph | SYSTEMS | hyper-EM condition | VARIABLES

Journal Article

2009 Asia-Pacific Conference on Information Processing, 07/2009, Volume 1, pp. 285 - 287

Diameter of an undirected graph is the maximal distance between any two vertices. We can obtain a digraph (directed graph) by presenting a direction for each...

orientation | Bipartite graph | diameter | digraph | split graph | Information processing | Split graph | Digraph | Orientation | Diameter

orientation | Bipartite graph | diameter | digraph | split graph | Information processing | Split graph | Digraph | Orientation | Diameter

Conference Proceeding

2016, Graduate studies in mathematics, ISBN 9781470423070, Volume 174, xii, 295 pages

Book

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 01/2013, Volume 103, Issue 1, pp. 184 - 208

The generating function that records the sizes of directed circuit partitions of a connected 2-in, 2-out digraph D can be determined from the interlacement...

Split graph | Circuit partition | Pivoting | Isotropic system | Interlace polynomial | Local complementation | NUMBER | WALKS | DECOMPOSITION | LINKS | FORMULA | CIRCLE | CIRCUITS | MATHEMATICS | LINEAR ALGEBRA | EULER TRAILS | GRAPH POLYNOMIALS

Split graph | Circuit partition | Pivoting | Isotropic system | Interlace polynomial | Local complementation | NUMBER | WALKS | DECOMPOSITION | LINKS | FORMULA | CIRCLE | CIRCUITS | MATHEMATICS | LINEAR ALGEBRA | EULER TRAILS | GRAPH POLYNOMIALS

Journal Article

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