Discrete Applied Mathematics, ISSN 0166-218X, 12/2019, Volume 271, pp. 25 - 48

For any class C of bipartite graphs, we define quasi-C to be the class of all graphs G such that every bipartition of G belongs to C. This definition is...

Bipartite permutation graph | Monotone graph | Hereditary graph class | Switch Markov chain | Polynomial time recognition | MATHEMATICS, APPLIED | Permutations | Markov chains | Graphs | Polynomials | Algorithms | Binary system

Bipartite permutation graph | Monotone graph | Hereditary graph class | Switch Markov chain | Polynomial time recognition | MATHEMATICS, APPLIED | Permutations | Markov chains | Graphs | Polynomials | Algorithms | Binary system

Journal Article

Discrete Mathematics, ISSN 0012-365X, 08/2019, Volume 342, Issue 8, pp. 2415 - 2428

In this paper, we introduce the Pell graphs, a new family of graphs similar to the Fibonacci cubes. They are defined on certain ternary strings (Pell strings)...

Fibonacci cube | Bipartite graph | Median graph | Subhypercube | Hypercube | MATHEMATICS | FIBONACCI CUBES | LUCAS | ENUMERATIVE PROPERTIES

Fibonacci cube | Bipartite graph | Median graph | Subhypercube | Hypercube | MATHEMATICS | FIBONACCI CUBES | LUCAS | ENUMERATIVE PROPERTIES

Journal Article

Discrete Mathematics, ISSN 0012-365X, 11/2013, Volume 313, Issue 21, pp. 2390 - 2400

One method of graph decomposition is to define a binary operation on the set of graphs and to represent graphs as products of prime elements with respect to...

Graph decomposition | Bipartite chain graphs | NLC-width | [formula omitted]-threshold graphs | Finite list of forbidden induced subgraphs | Canonical decomposition | Threshold-width | Difference graphs | Threshold graphs | Clique-width | H-threshold graphs | RECOGNITION | SEQUENCES | DECOMPOSITION | MATHEMATICS

Graph decomposition | Bipartite chain graphs | NLC-width | [formula omitted]-threshold graphs | Finite list of forbidden induced subgraphs | Canonical decomposition | Threshold-width | Difference graphs | Threshold graphs | Clique-width | H-threshold graphs | RECOGNITION | SEQUENCES | DECOMPOSITION | MATHEMATICS

Journal Article

Journal of Intelligent and Fuzzy Systems, ISSN 1064-1246, 2019, Volume 36, Issue 2, pp. 1917 - 1925

For a graph G = (V, E) the L(3, 1, 1)-labeling is a mapping mu from the vertex set V to the set of non-negative integers {0, 1, 2, ...} such that vertical bar...

1)-labeling | Square of complete bipartite graphs | Square of paths | Frequency assignment | Square of complete graphs | L(3,1,1)-labeling | square of paths | square of complete bipartite graphs | PRODUCT | INTUITIONISTIC FUZZY GRAPHS | square of complete graphs | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Integers | Apexes | Labelling | Graphs | Mapping | Graph theory | Labeling

1)-labeling | Square of complete bipartite graphs | Square of paths | Frequency assignment | Square of complete graphs | L(3,1,1)-labeling | square of paths | square of complete bipartite graphs | PRODUCT | INTUITIONISTIC FUZZY GRAPHS | square of complete graphs | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | Integers | Apexes | Labelling | Graphs | Mapping | Graph theory | Labeling

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 2018, Volume 775, p. 16

We investigate the terminal-pairability problem in the case when the base graph is a complete bipartite graph, and the demand graph is a (not necessarily...

Terminal-pairability | Complete bipartite graph | Edge-disjoint paths

Terminal-pairability | Complete bipartite graph | Edge-disjoint paths

Journal Article

Journal of Computer and System Sciences, ISSN 0022-0000, 11/2017, Volume 89, pp. 410 - 431

The Colouring problem is that of deciding, given a graph G and an integer k, whether G admits a (proper) k-colouring. For all graphs H up to five vertices, we...

Forbidden induced subgraph | Graph colouring | Diamond-free | Clique-width | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | CO-GEM-FREE | TRIANGLE-FREE GRAPHS | LINEAR-TIME | BOUNDED CLIQUE-WIDTH | COMPUTER SCIENCE, THEORY & METHODS | HEREDITARY CLASSES | FORBIDDEN SUBGRAPHS | BIPARTITE GRAPHS | Logic | Mathematics

Forbidden induced subgraph | Graph colouring | Diamond-free | Clique-width | COMPUTER SCIENCE, HARDWARE & ARCHITECTURE | CO-GEM-FREE | TRIANGLE-FREE GRAPHS | LINEAR-TIME | BOUNDED CLIQUE-WIDTH | COMPUTER SCIENCE, THEORY & METHODS | HEREDITARY CLASSES | FORBIDDEN SUBGRAPHS | BIPARTITE GRAPHS | Logic | Mathematics

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 08/2019, Volume 266, pp. 171 - 185

A proper edge coloring of a graph G with colors 1,2,…,t is called a cyclic intervalt-coloring if for each vertex v of G the edges incident to v are colored by...

Cyclic interval edge coloring | Interval edge coloring | Deficiency | Cyclic deficiency | Edge coloring | INTERVAL EDGE-COLORINGS | MATHEMATICS, APPLIED | BIPARTITE GRAPHS | Graphs | Graph theory | Graph coloring | Apexes | Naturvetenskap | Diskret matematik | Edge coloring; Interval edge coloring; Cyclic interval edge coloring; Deficiency; Cyclic deficiency | Mathematics | Natural Sciences | Matematik | Discrete Mathematics

Cyclic interval edge coloring | Interval edge coloring | Deficiency | Cyclic deficiency | Edge coloring | INTERVAL EDGE-COLORINGS | MATHEMATICS, APPLIED | BIPARTITE GRAPHS | Graphs | Graph theory | Graph coloring | Apexes | Naturvetenskap | Diskret matematik | Edge coloring; Interval edge coloring; Cyclic interval edge coloring; Deficiency; Cyclic deficiency | Mathematics | Natural Sciences | Matematik | Discrete Mathematics

Journal Article

IEEE Transactions on Knowledge and Data Engineering, ISSN 1041-4347, 01/2017, Volume 29, Issue 1, pp. 57 - 71

The bipartite graph is a ubiquitous data structure that can model the relationship between two entity types: for instance, users and items, queries and...

Bridges | Bipartite graph ranking | popularity prediction | Probabilistic logic | graph regularization | Data models | Bipartite graph | Bayes methods | Electronic mail | personalized recommendation | Kernel | n-partite graphs | COMPUTER SCIENCE, INFORMATION SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Bayes' theorem | Usage | Graph theory | Graphs | Queries | Ranking

Bridges | Bipartite graph ranking | popularity prediction | Probabilistic logic | graph regularization | Data models | Bipartite graph | Bayes methods | Electronic mail | personalized recommendation | Kernel | n-partite graphs | COMPUTER SCIENCE, INFORMATION SYSTEMS | COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE | ENGINEERING, ELECTRICAL & ELECTRONIC | Bayes' theorem | Usage | Graph theory | Graphs | Queries | Ranking

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 10/2016, Volume 506, pp. 279 - 307

We study the concept of the Coxeter energy of graphs and digraphs (quivers) as an analogue of Gutman's adjacency energy, which has applications in theoretical...

Coxeter polynomial | Graph energy | Salem tree | Dynkin graphs | Coxeter matrix | Graph eigenvalues | Coxeter energy | Tree | SPECTRAL CLASSIFICATION | MATHEMATICS, APPLIED | PI-ELECTRON ENERGY | LAPLACIAN ENERGY | MAHLER MEASURE | MATHEMATICS | EIGENVALUES | COMPUTING GRAM CONGRUENCES | ALGEBRAS | TREES | EDGE-BIPARTITE GRAPHS | TRANSFORMATIONS | Algebra

Coxeter polynomial | Graph energy | Salem tree | Dynkin graphs | Coxeter matrix | Graph eigenvalues | Coxeter energy | Tree | SPECTRAL CLASSIFICATION | MATHEMATICS, APPLIED | PI-ELECTRON ENERGY | LAPLACIAN ENERGY | MAHLER MEASURE | MATHEMATICS | EIGENVALUES | COMPUTING GRAM CONGRUENCES | ALGEBRAS | TREES | EDGE-BIPARTITE GRAPHS | TRANSFORMATIONS | Algebra

Journal Article

Discrete Applied Mathematics, ISSN 0166-218X, 12/2019, Volume 271, pp. 171 - 183

A proper k-coloring with colors 1,2,…,k of a graph G=(V,E) is an ordered partition (V1,V2,…,Vk) of V such that Vi is an independent set or color class in which...

Star-convex bipartite graphs | Perfect elimination bipartite graphs | Chordal graphs | Partial Grundy coloring | NP-completeness | Polynomial time algorithms | MATHEMATICS, APPLIED | Coloring | Codes | Algorithms | Upper bounds | Binary system | Color | Graphs

Star-convex bipartite graphs | Perfect elimination bipartite graphs | Chordal graphs | Partial Grundy coloring | NP-completeness | Polynomial time algorithms | MATHEMATICS, APPLIED | Coloring | Codes | Algorithms | Upper bounds | Binary system | Color | Graphs

Journal Article

Theoretical Computer Science, ISSN 0304-3975, 02/2020, Volume 806, pp. 402 - 415

•We study vertex labelings of bipartite graphs by strings, edges representing overlaps.•The corresponding parameter called readability denotes the minimum...

Grid graph | Bipartite graph | Readability | Euler's totient function

Grid graph | Bipartite graph | Readability | Euler's totient function

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 10/2013, Volume 61, Issue 19, pp. 4673 - 4685

This paper extends previous results on wavelet filterbanks for data defined on graphs from the case of orthogonal transforms to more general and flexible...

Wavelet transforms | sampling in graphs | wavelet filterbanks on graphs | bipartite subgraph decompositions | Eigenvalues and eigenfunctions | Bipartite graph | Approximation methods | Image reconstruction | Spectral analysis | Network theory (graphs) | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Innovations | Electric filters | Signal processing | Graph theory | Design and construction | Graphs | Wavelet | Reconstruction | Transforms | Spectra | Decomposition | Standards

Wavelet transforms | sampling in graphs | wavelet filterbanks on graphs | bipartite subgraph decompositions | Eigenvalues and eigenfunctions | Bipartite graph | Approximation methods | Image reconstruction | Spectral analysis | Network theory (graphs) | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Innovations | Electric filters | Signal processing | Graph theory | Design and construction | Graphs | Wavelet | Reconstruction | Transforms | Spectra | Decomposition | Standards

Journal Article

Discrete Mathematics, ISSN 0012-365X, 01/2016, Volume 339, Issue 1, pp. 391 - 398

A strong edge-coloring of a graph G is an assignment of colors to edges such that every color class induces a matching. We here focus on bipartite graphs whose...

Bipartite graphs | Strong edge-coloring | Complexity | INDUCED MATCHINGS | MATHEMATICS | STRONG CHROMATIC INDEX | Computer Science | Discrete Mathematics

Bipartite graphs | Strong edge-coloring | Complexity | INDUCED MATCHINGS | MATHEMATICS | STRONG CHROMATIC INDEX | Computer Science | Discrete Mathematics

Journal Article

Discrete Mathematics, ISSN 0012-365X, 02/2020, Volume 343, Issue 2, p. 111663

The classical Ore’s Theorem states that every graph G of order n≥3 with σ2(G)≥n is hamiltonian, where σ2(G)=min{dG(x)+dG(y):x,y∈V(G),x≠y,xy∉E(G)}. Recently,...

Hamiltonian cycle | Ore’s Theorem | Bipartite graph | MATHEMATICS | Ore's Theorem

Hamiltonian cycle | Ore’s Theorem | Bipartite graph | MATHEMATICS | Ore's Theorem

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 07/2014, Volume 62, Issue 14, pp. 3578 - 3590

This paper proposes M-channel oversampled filter banks for graph signals. The filter set satisfies the perfect reconstruction condition. A method of designing...

Wavelet transforms | Laplace equations | Graph filter banks | graph signal denoising | Bipartite graph | Spectral analysis | Image reconstruction | graph signal processing | graph wavelets | oversampled filter banks | PERFECT RECONSTRUCTION FILTERBANKS | LATTICE STRUCTURE | TRANSFORM | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Usage | Graph theory | Laplace transformation | Numerical analysis | Innovations | Reconstruction | Design engineering | Redundancy | Noise reduction | Filter banks | Graphs | Transaction processing

Wavelet transforms | Laplace equations | Graph filter banks | graph signal denoising | Bipartite graph | Spectral analysis | Image reconstruction | graph signal processing | graph wavelets | oversampled filter banks | PERFECT RECONSTRUCTION FILTERBANKS | LATTICE STRUCTURE | TRANSFORM | ENGINEERING, ELECTRICAL & ELECTRONIC | Signal processing | Usage | Graph theory | Laplace transformation | Numerical analysis | Innovations | Reconstruction | Design engineering | Redundancy | Noise reduction | Filter banks | Graphs | Transaction processing

Journal Article

Discrete Mathematics, ISSN 0012-365X, 06/2020, Volume 343, Issue 6, p. 111834

Using an algebraic characterization of circle graphs, Bouchet proved in 1999 that if a bipartite graph G is the complement of a circle graph, then G is a...

Complementation | Bipartite graphs | Circle graphs

Complementation | Bipartite graphs | Circle graphs

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 11/2017, Volume 532, pp. 222 - 230

We consider only connected bipartite graphs G with a unique perfect matching M. Let Gw be the weighted graph obtained from G by giving weights to its edges...

Adjacency matrix | Inverse graph | Unique perfect matching | Weighted graph | MATHEMATICS | MATHEMATICS, APPLIED | TREES | BIPARTITE GRAPHS

Adjacency matrix | Inverse graph | Unique perfect matching | Weighted graph | MATHEMATICS | MATHEMATICS, APPLIED | TREES | BIPARTITE GRAPHS

Journal Article

Graphs and Combinatorics, ISSN 0911-0119, 9/2019, Volume 35, Issue 5, pp. 1169 - 1177

A dominating set of a graph G is a set $$D\subseteq V_G$$ D ⊆ V G such that every vertex in $$V_G-D$$ V G - D is adjacent to at least one vertex in D, and the...

05C76 | Domination number | Bipartization | Mathematics | Engineering Design | Bipartite graph | Combinatorics | 05C69 | 05C05 | MATHEMATICS | EQUAL DOMINATION | Graphs | Mathematics - Combinatorics

05C76 | Domination number | Bipartization | Mathematics | Engineering Design | Bipartite graph | Combinatorics | 05C69 | 05C05 | MATHEMATICS | EQUAL DOMINATION | Graphs | Mathematics - Combinatorics

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 12/2014, Volume 62, Issue 24, pp. 6425 - 6437

We describe a method of oversampling signals defined on a weighted graph by using an oversampled graph Laplacian matrix. The conventional method of using...

Laplace equations | Graph filter banks | Transforms | graph oversampling | Licenses | Signal processing | multiresolution | Eigenvalues and eigenfunctions | Bipartite graph | Matrix decomposition | graph signal processing | graph wavelets | ENGINEERING, ELECTRICAL & ELECTRONIC | Measurement | Usage | Frequency modulation | Innovations | Graph theory | Laplace transformation | Graphs | Filter banks | Transformations | Spectra | Decomposition | Transaction processing | Oversampling

Laplace equations | Graph filter banks | Transforms | graph oversampling | Licenses | Signal processing | multiresolution | Eigenvalues and eigenfunctions | Bipartite graph | Matrix decomposition | graph signal processing | graph wavelets | ENGINEERING, ELECTRICAL & ELECTRONIC | Measurement | Usage | Frequency modulation | Innovations | Graph theory | Laplace transformation | Graphs | Filter banks | Transformations | Spectra | Decomposition | Transaction processing | Oversampling

Journal Article

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Full Text
Counting degree sequences of spanning trees in bipartite graphs: A graph‐theoretic proof

Journal of Graph Theory, ISSN 0364-9024, 11/2019, Volume 92, Issue 3, pp. 230 - 236

Given a bipartite graph G = ( S ∪ ˙ T , E ) with bipartition S , T each spanning tree in G has a degree sequence on S and one on T. Löhne and Rudloff showed...

degree sequences | spanning trees | bipartite graphs | MATHEMATICS

degree sequences | spanning trees | bipartite graphs | MATHEMATICS

Journal Article

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