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Graphs and Combinatorics, ISSN 0911-0119, 11/2018, Volume 34, Issue 6, pp. 1333 - 1346
We derive a simple bijection between geometric plane perfect matchings on 2n points in convex position and triangulations on n + 2 points in convex position.... 
Temperley–Lieb algebras | Triangulations | Fuss–Catalan algebras | Perfect matchings | MATHEMATICS | MODELS | Temperley-Lieb algebras | Fuss-Catalan algebras | FUSS | Algebra | Apexes
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 03/2013, Volume 103, Issue 2, pp. 291 - 305
We determine the minimum vertex degree that ensures a perfect matching in a 3-uniform hypergraph. More precisely, suppose that H is a sufficiently large... 
Hypergraphs | Perfect matchings | MATHEMATICS | UNIFORM HYPERGRAPHS | LARGE MINIMUM DEGREE | PERFECT MATCHINGS | INDEPENDENT EDGES
Journal Article
Journal of Combinatorial Theory, Series B, ISSN 0095-8956, 01/2016, Volume 116, pp. 333 - 366
A perfect matching in a 4-uniform hypergraph on n vertices is a subset of ⌊n4⌋ disjoint edges. We prove that if H is a sufficiently large 4-uniform hypergraph... 
Hypergraphs | Vertex degree | Perfect matching | MATHEMATICS | 3-UNIFORM HYPERGRAPHS | LARGE MINIMUM DEGREE | UNIFORM HYPERGRAPHS | GRAPHS
Journal Article
Journal of Graph Theory, ISSN 0364-9024, 04/2019, Volume 90, Issue 4, pp. 535 - 546
A graph G is matching‐covered if every edge of G is contained in a perfect matching. A matching‐covered graph G is strongly coverable if, for any edge e of G,... 
matching‐covered graph | perfect matching | matching-covered graph | MATHEMATICS | EAR-DECOMPOSITIONS
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2016, Volume 30, Issue 3, pp. 1351 - 1357
We prove a new upper bound for the minimum d-degree threshold for perfect matchings in k-uniform hypergraphs when d < k/2. As a consequence, this determines... 
Hypergraph | Perfect matching | Erdös matching conjecture | MATHEMATICS, APPLIED | perfect matching | MINIMUM DEGREE THRESHOLDS | hypergraph | Erdos matching conjecture | UNIFORM HYPERGRAPHS
Journal Article
Computational Geometry: Theory and Applications, ISSN 0925-7721, 09/2015, Volume 48, Issue 8, pp. 622 - 633
For a set R of n red points and a set B of n blue points, a BR-matching is a non-crossing geometric perfect matching where each segment has one endpoint in B... 
Reconfiguration problem | Compatible matchings | Transformation graph | Bichromatic point set | Perfect matchings | MATHEMATICS | MATHEMATICS, APPLIED | SPANNING-TREES
Journal Article
Discrete Mathematics, ISSN 0012-365X, 06/2019, Volume 342, Issue 6, pp. 1731 - 1737
A matching in a 3-uniform hypergraph is a set of pairwise disjoint edges. We use E3(2d−1,n−2d+1) to denote the 3-uniform hypergraph whose vertex set can be... 
Matching | 3-uniform hypergraph | Adjacent vertices | HAMILTON CYCLES | MATHEMATICS | PERFECT MATCHINGS | THEOREM | MINIMUM DEGREE THRESHOLDS | ERDOS | UNIFORM HYPERGRAPHS
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 02/2016, Volume 615, pp. 91 - 101
The strong matching preclusion number of a graph is the minimum number of vertices and edges whose deletion results in a graph that has neither perfect... 
[formula omitted]-star graphs | Perfect matching | Almost perfect matching | (n, k)-star graphs | FAULT HAMILTONICITY | COMPUTER SCIENCE, THEORY & METHODS | ALTERNATING GROUP GRAPHS | Matching | Stars | Deletion | Graphs | Graph theory | Parks | Optimization
Journal Article
Information Sciences, ISSN 0020-0255, 2009, Volume 179, Issue 8, pp. 1092 - 1101
The matching preclusion number of a graph is the minimum number of edges whose deletion results in a graph that has neither perfect matchings nor... 
Hypercubes | Perfect matching | Almost-perfect matching | Interconnection networks | COMPUTER SCIENCE, INFORMATION SYSTEMS | NETWORKS | FOLDED HYPERCUBES
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 10/2011, Volume 412, Issue 45, pp. 6409 - 6419
The matching preclusion problem, introduced by Brigham et al. [R.C. Brigham, F. Harary, E.C. Violin, and J. Yellen, Perfect-matching preclusion, Congressus... 
Perfect and almost perfect matching | Matching preclusion | Recursive circulant | Restricted hypercube-like graph | Vertex and/or edge deletion | PERFECT MATCHINGS | COMPUTER SCIENCE, THEORY & METHODS | INTERCONNECTION NETWORKS | Matching | Deletion | Graphs | Violins
Journal Article
Random Structures & Algorithms, ISSN 1042-9832, 09/2019, Volume 55, Issue 2, pp. 271 - 289
Journal Article
Leibniz International Proceedings in Informatics, LIPIcs, ISSN 1868-8969, 06/2018, Volume 101, pp. 71 - 713
Conference Proceeding
Discrete Applied Mathematics, ISSN 0166-218X, 08/2019, Volume 266, pp. 153 - 162
A connected plane cubic graph is called an m-barrel fullerene and denoted by F(m,k), if it has the following structure: The first circle is an m-gon. Then the... 
m-barrel fullerene | Fullerene graph | Perfect matchings | MATHEMATICS, APPLIED | WALKS | Fullerenes | Graphs | Enumeration | Asymptotic properties | Hexagons | Asymptotic methods | Combinatorics | Mathematics
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 12/2012, Volume 465, pp. 10 - 20
Matching preclusion is a measure of robustness in the event of edge failure in interconnection networks. The matching preclusion number of a graph G is the... 
Almost perfect matching | Perfect matching | Matching preclusion set | Balanced hypercubes | COMPUTER SCIENCE, THEORY & METHODS | INTERCONNECTION NETWORKS
Journal Article
Theoretical Computer Science, ISSN 0304-3975, 02/2019, Volume 759, pp. 61 - 71
The matching preclusion number of a graph G, denoted by mp(G), is the minimum number of edges whose deletion results in a graph that has neither perfect... 
Nordhaus–Gaddum problem | Perfect matching | Extremal problem | Matching preclusion number | Interconnection networks | COMPUTER SCIENCE, THEORY & METHODS | Nordhaus-Gaddum problem
Journal Article
Random Structures & Algorithms, ISSN 1042-9832, 07/2019, Volume 54, Issue 4, pp. 797 - 819
Let {Gi} be the random graph process: starting with an empty graph G0 with n vertices, in every step i ≥ 1 the graph Gi is formed by taking an edge chosen... 
random graphs | hitting time | perfect matchings | local resilience | Hamiltonicity | EXISTENCE | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | THEOREM | CYCLES | Apexes | Graph theory | Resilience
Journal Article
SIAM Journal on Discrete Mathematics, ISSN 0895-4801, 2018, Volume 32, Issue 1, pp. 522 - 533
The minimum codegree threshold for a perfect matching in a k-graph with n vertices was determined by Rodl, Rucinski, and Szemeredi for the case when n... 
Hypergraph | Almost perfect matching | Minimum codegree | MATHEMATICS, APPLIED | almost perfect matching | MINIMUM DEGREE THRESHOLDS | hypergraph | UNIFORM HYPERGRAPHS | minimum codegree
Journal Article
by Jie Han
Transactions of the American Mathematical Society, ISSN 0002-9947, 07/2017, Volume 369, Issue 7, pp. 5197 - 5218
For any \gamma >0, Keevash, Knox and Mycroft (2015) constructed a polynomial-time algorithm which determines the existence of perfect matchings in any n-vertex... 
Hypergraph | Perfect matching | Absorbing method | VERTEX DEGREE | MATHEMATICS | hypergraph | 3-UNIFORM HYPERGRAPHS | absorbing method | COMPLEXITY | MINIMUM DEGREE THRESHOLDS | CODEGREE
Journal Article
Discrete Applied Mathematics, ISSN 0166-218X, 05/2019, Volume 261, pp. 22 - 27
Consider a situation in which individuals –the buyers –have different valuations for the products of a given set. An envy-free assignment of product items to... 
Assignment | Shortest path problem | Walrasian equilibrium | Perfect matching | Envy-free pricing | MATHEMATICS, APPLIED | CONJOINT | OPTIMIZATION | Valuation | Pricing | Purchasing
Journal Article
Random Structures & Algorithms, ISSN 1042-9832, 05/2018, Volume 52, Issue 3, pp. 367 - 378
We introduce a new procedure for generating the binomial random graph/hypergraph models, referred to as online sprinkling. As an illustrative application of... 
Perfect matching | hypergraph | random graphs | COMPUTER SCIENCE, SOFTWARE ENGINEERING | MATHEMATICS | MATHEMATICS, APPLIED | Graphs | Graph theory | Sprinkling
Journal Article
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