Journal of Graph Theory, ISSN 0364-9024, 11/2019, Volume 92, Issue 3, pp. 304 - 321

An odd graph is a graph whose vertex degrees are all odd. As introduced by Pyber in 1991, an odd edge‐covering of graph G is a family of odd subgraphs that...

odd edge‐coloring | odd subgraph | T‐join | odd edge‐covering | T-join | MATHEMATICS | odd edge-covering | odd edge-coloring

odd edge‐coloring | odd subgraph | T‐join | odd edge‐covering | T-join | MATHEMATICS | odd edge-covering | odd edge-coloring

Journal Article

ELECTRONIC JOURNAL OF COMBINATORICS, ISSN 1077-8926, 07/2017, Volume 24, Issue 3

We characterize the class of infinite connected graphs G for which there exists a T-join for any choice of an infinite T subset of V(G). We also show that the...

T-join | MATHEMATICS | infinite graph | MATHEMATICS, APPLIED

T-join | MATHEMATICS | infinite graph | MATHEMATICS, APPLIED

Journal Article

Mathematical Programming, ISSN 0025-5610, 11/2018, Volume 172, Issue 1, pp. 191 - 207

We consider the s–t-path TSP: given a finite metric space with two elements s and t, we look for a path from s to t that contains all the elements and has...

Convex combination | 68Q25 | Theoretical, Mathematical and Computational Physics | 68R05 | Mathematics | 90C59 | 90C27 | Approximation algorithm | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Spanning tree | Traveling salesman problem | T -join | Combinatorics | 05C05 | T-join | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | Management science | Algorithms | Metric space | Graph theory

Convex combination | 68Q25 | Theoretical, Mathematical and Computational Physics | 68R05 | Mathematics | 90C59 | 90C27 | Approximation algorithm | Mathematical Methods in Physics | Calculus of Variations and Optimal Control; Optimization | Mathematics of Computing | Numerical Analysis | Spanning tree | Traveling salesman problem | T -join | Combinatorics | 05C05 | T-join | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | ALGORITHM | Management science | Algorithms | Metric space | Graph theory

Journal Article

Discrete Mathematics, ISSN 0012-365X, 03/2018, Volume 341, Issue 3, pp. 606 - 626

Motivated by a relaxed notion of the celebrated Hamiltonian cycle, this paper investigates its variant, parity Hamiltonian cycle (PHC): A PHC of a graph is a...

[formula omitted]-join | Graph factor | Hamiltonian cycle problem | T-join | MATHEMATICS | COMBINATORIAL OPTIMIZATION | DISJOINT SPANNING-TREES | GRAPHS

[formula omitted]-join | Graph factor | Hamiltonian cycle problem | T-join | MATHEMATICS | COMBINATORIAL OPTIMIZATION | DISJOINT SPANNING-TREES | GRAPHS

Journal Article

Algorithmica, ISSN 0178-4617, 1/2016, Volume 74, Issue 1, pp. 270 - 325

The undirected negative cost cycle detection (UNCCD) problem is concerned with checking whether an undirected, weighted graph contains a negative cost cycle....

Negative cost cycle | All pairs shortest path | T$$ T -join | Theory of Computation | b$$ b -Matching | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | Undirected graphs | Algorithm Analysis and Problem Complexity | Perfect matching | T-join | b-Matching | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | PATHS | MATCHING PROBLEMS | GRAPHS | Analysis

Negative cost cycle | All pairs shortest path | T$$ T -join | Theory of Computation | b$$ b -Matching | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | Mathematics of Computing | Computer Science | Undirected graphs | Algorithm Analysis and Problem Complexity | Perfect matching | T-join | b-Matching | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | PATHS | MATCHING PROBLEMS | GRAPHS | Analysis

Journal Article

Discrete Mathematics, ISSN 0012-365X, 02/2016, Volume 339, Issue 2, pp. 547 - 559

A connected undirected graph G is a Seymour graph if the maximum number of edge disjoint T-cuts is equal to the cardinality of a minimum T-join for every even...

Seymour graph | [formula omitted]-join | Join covered graph | Conservative function | Matching covered graph | T-join | MATHEMATICS

Seymour graph | [formula omitted]-join | Join covered graph | Conservative function | Matching covered graph | T-join | MATHEMATICS

Journal Article

ACM Transactions on Algorithms (TALG), ISSN 1549-6325, 07/2018, Volume 14, Issue 3, pp. 1 - 80

This article shows the weighted matching problem on general graphs can be solved in time O ( n ( m + n log n )) for n and m the number of vertices and edges,...

Matching | T-join | blossom | f -factor | b -matching | shortest-paths tree | degree-constrained subgraph | conservative graph | Conservative graph | B-matching | F-factor | Degree-constrained subgraph | Blossom | Shortest-paths tree | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | MINIMUM SPANNING-TREES | ALGORITHMS | GRAPHS | LINEAR-TIME | f-factor | SENSITIVITY-ANALYSIS | COMPUTER SCIENCE, THEORY & METHODS | b-matching

Matching | T-join | blossom | f -factor | b -matching | shortest-paths tree | degree-constrained subgraph | conservative graph | Conservative graph | B-matching | F-factor | Degree-constrained subgraph | Blossom | Shortest-paths tree | MATHEMATICS, APPLIED | EFFICIENT IMPLEMENTATION | MINIMUM SPANNING-TREES | ALGORITHMS | GRAPHS | LINEAR-TIME | f-factor | SENSITIVITY-ANALYSIS | COMPUTER SCIENCE, THEORY & METHODS | b-matching

Journal Article

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2013, Volume 7801, pp. 362 - 374

Conference Proceeding

Ars Mathematica Contemporanea, ISSN 1855-3966, 2016, Volume 10, Issue 2, pp. 359 - 370

An edge-coloring of a graph G is said to be odd if for each vertex v of G and each color c, the vertex v either uses the color c an odd number of times or does...

T-join | Subcubic graph | Odd chromatic index | Odd edge-covering | Odd edge-coloring | MATHEMATICS | MATHEMATICS, APPLIED | odd edge-coloring | odd chromatic index | odd edge-covering

T-join | Subcubic graph | Odd chromatic index | Odd edge-covering | Odd edge-coloring | MATHEMATICS | MATHEMATICS, APPLIED | odd edge-coloring | odd chromatic index | odd edge-covering

Journal Article

Discrete Mathematics, Algorithms and Applications, ISSN 1793-8309, 12/2017, Volume 9, Issue 6

Journal Article

Algorithmica, ISSN 0178-4617, 5/2015, Volume 72, Issue 1, pp. 126 - 147

We design and analyse approximation algorithms for the minimum-cost connected T-join problem: given an undirected graph G=(V,E) with nonnegative costs on the...

s , t -Path TSP | Theory of Computation | Primal-dual method | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | T -Joins | LP rounding | Mathematics of Computing | Computer Science | Approximation algorithms | Algorithm Analysis and Problem Complexity | Prize-collecting problems | Traveling Salesman Problem | s,t-Path TSP | T-Joins | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | TREES | PATHS | s, t-Path TSP | ALGORITHMS

s , t -Path TSP | Theory of Computation | Primal-dual method | Computer Systems Organization and Communication Networks | Data Structures, Cryptology and Information Theory | Algorithms | T -Joins | LP rounding | Mathematics of Computing | Computer Science | Approximation algorithms | Algorithm Analysis and Problem Complexity | Prize-collecting problems | Traveling Salesman Problem | s,t-Path TSP | T-Joins | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS, APPLIED | TREES | PATHS | s, t-Path TSP | ALGORITHMS

Journal Article

Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 01/2016, Volume 116, pp. 287 - 305

Let G be a plane graph and T an even subset of its vertices. It has been conjectured that if all T-cuts of G have the same parity and the size of every T-cut...

Edge-coloring | Planar graphs | T-joins | MATHEMATICS | Computer science

Edge-coloring | Planar graphs | T-joins | MATHEMATICS | Computer science

Journal Article

Mathematics of Operations Research, ISSN 0364-765X, 05/2004, Volume 29, Issue 2, pp. 383 - 393

We study generators of metric spacessets of points with the property that every point of the space is uniquely determined by the distances from their...

metric space | join | combinatorial search | T | false coins | isometric embedding of graphs | Leaves | Mathematical theorems | Cardinality | Coordinate systems | Mathematics | Polynomials | Mathematical functions | Mathematical vectors | Combinatorics | Vertices | Combinatorial search | T-join | Isometric embedding of graphs | Join | Metric space | False coins | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CUTS | Management science | Research | Graphic methods | Studies | Graphs | Life Sciences | Other

metric space | join | combinatorial search | T | false coins | isometric embedding of graphs | Leaves | Mathematical theorems | Cardinality | Coordinate systems | Mathematics | Polynomials | Mathematical functions | Mathematical vectors | Combinatorics | Vertices | Combinatorial search | T-join | Isometric embedding of graphs | Join | Metric space | False coins | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | CUTS | Management science | Research | Graphic methods | Studies | Graphs | Life Sciences | Other

Journal Article

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), ISSN 0302-9743, 2016, Volume 9849, pp. 50 - 58

Conference Proceeding

Journal of Graph Theory, ISSN 0364-9024, 09/2007, Volume 56, Issue 1, pp. 64 - 71

In an earlier paper 3, we studied cycles in graphs that intersect all edge‐cuts of prescribed sizes. Passing to a more general setting, we examine the...

contraction | graft | small edge‐cut | T‐join | A‐covering join | T-join | A-covering join | Graft | Contraction | Small edge-cut | MATHEMATICS | small edge-cut

contraction | graft | small edge‐cut | T‐join | A‐covering join | T-join | A-covering join | Graft | Contraction | Small edge-cut | MATHEMATICS | small edge-cut

Journal Article

International Journal of Computer Mathematics, ISSN 0020-7160, 09/2011, Volume 88, Issue 13, pp. 2685 - 2696

Strong product G 1 ⊠ G 2 of two graphs G 1 and G 2 has a vertex set V(G 1 )×V(G 2 ) and two vertices (u 1 , v 1 ) and (u 2 , v 2 ) are adjacent whenever u 1 =u...

T-join | 05C76 | strong product | factor-criticality | perfect matching | 05C70 | product graph | MATHEMATICS, APPLIED | L-EXTENDIBLE GRAPH | Graphs | Mathematical models

T-join | 05C76 | strong product | factor-criticality | perfect matching | 05C70 | product graph | MATHEMATICS, APPLIED | L-EXTENDIBLE GRAPH | Graphs | Mathematical models

Journal Article

SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2012, Volume 26, Issue 3, pp. 884 - 895

Let nu(G) be the maximum number of vertex-disjoint odd cycles of a graph G and tau(G) the minimum number of vertices whose removal makes G bipartite. We show...

Odd cycle transversals | Erdo″s-Pósa property | Planar graphs | T-joins | MATHEMATICS, APPLIED | planar graphs | odd cycle transversals | Erdos-Posa property | TRIANGLES | CONJECTURE

Odd cycle transversals | Erdo″s-Pósa property | Planar graphs | T-joins | MATHEMATICS, APPLIED | planar graphs | odd cycle transversals | Erdos-Posa property | TRIANGLES | CONJECTURE

Journal Article

Computational Optimization and Applications, ISSN 0926-6003, 1/2012, Volume 51, Issue 1, pp. 323 - 344

The max-cut problem asks for partitioning the nodes V of a graph G=(V,E) into two sets (one of which might be empty), such that the sum of weights of edges...

T-join | Convex and Discrete Geometry | Operations Research/Decision Theory | Planar graph | Maximum cut | Mathematics | Operations Research, Management Science | Kasteleyn city | Statistics, general | Perfect matching | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SEPARATOR THEOREM | ALGORITHM | LAYOUT | OPTIMIZATION | GROUND-STATES | Computer science | Algorithms | Studies | Matching | Partitioning | Computation | Running | Graphs | Inverse | Combinatorial analysis

T-join | Convex and Discrete Geometry | Operations Research/Decision Theory | Planar graph | Maximum cut | Mathematics | Operations Research, Management Science | Kasteleyn city | Statistics, general | Perfect matching | Optimization | MATHEMATICS, APPLIED | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SEPARATOR THEOREM | ALGORITHM | LAYOUT | OPTIMIZATION | GROUND-STATES | Computer science | Algorithms | Studies | Matching | Partitioning | Computation | Running | Graphs | Inverse | Combinatorial analysis

Journal Article

Operations Research Letters, ISSN 0167-6377, 07/2013, Volume 41, Issue 4, pp. 321 - 324

Given an undirected graph with nonnegative edge weights, the max–min weighted T-join problem is to find an even cardinality vertex subset T such that the...

Max–min optimization | Bottleneck problem | [formula omitted]-joins | Max-min optimization | T-joins | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUBMODULAR SET FUNCTIONS | OPTIMIZATION | Algorithms

Max–min optimization | Bottleneck problem | [formula omitted]-joins | Max-min optimization | T-joins | OPERATIONS RESEARCH & MANAGEMENT SCIENCE | SUBMODULAR SET FUNCTIONS | OPTIMIZATION | Algorithms

Journal Article

Bulletin of the Malaysian Mathematical Sciences Society, ISSN 0126-6705, 2010, Volume 33, Issue 2, pp. 197 - 204

Lexicographic product G o H of two graphs G and H has vertex set V(G) x V(H) and two vertices (u(1), v(1)) and (u(2), v(2)) are adjacent whenever u(1)u(2) is...

Lexicographic product | T-join | Factor-criticality | Perfect matching | Extendable graph | MATHEMATICS | perfect matching | extendable graph | factor-criticality

Lexicographic product | T-join | Factor-criticality | Perfect matching | Extendable graph | MATHEMATICS | perfect matching | extendable graph | factor-criticality

Journal Article

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