Results 1 to 10 of about 704 (29)
Correlations in totally symmetric self‐complementary plane partitions
Transactions of the London Mathematical Society, Volume 8, Issue 1, Page 493-526, December 2021., 2021 Abstract Totally symmetric self‐complementary plane partitions (TSSCPPs) are boxed plane partitions with the maximum possible symmetry. We use the well‐known representation of TSSCPPs as a dimer model on a honeycomb graph enclosed in 1/12 of a hexagon with free boundary to express them as perfect matchings of a family of non‐bipartite planar graphs ...
Arvind Ayyer, Sunil Chhita
wiley +1 more source
Decomposing tournaments into paths
Proceedings of the London Mathematical Society, Volume 121, Issue 2, Page 426-461, August 2020., 2020 Abstract We consider a generalisation of Kelly's conjecture which is due to Alspach, Mason, and Pullman from 1976. Kelly's conjecture states that every regular tournament has an edge decomposition into Hamilton cycles, and this was proved by Kühn and Osthus for large tournaments. The conjecture of Alspach, Mason, and Pullman asks for the minimum number
Allan Lo +3 more
wiley +1 more source
The matching polynomial of a distance‐regular graph
International Journal of Mathematics and Mathematical Sciences, Volume 23, Issue 2, Page 89-97, 2000., 2000 A distance‐regular graph of diameter d has 2d intersection numbers that determine many properties of graph (e.g., its spectrum). We show that the first six coefficients of the matching polynomial of a distance‐regular graph can also be determined from its intersection array, and that this is the maximum number of coefficients so determined.
Robert A. Beezer, E. J. Farrell
wiley +1 more source
A Decomposition Theorem for Maximum Weight Bipartite Matchings [PDF]
, 1999 Let G be a bipartite graph with positive integer weights on the edges and without isolated nodes. Let n, N and W be the node count, the largest edge weight and the total weight of G. Let k(x,y) be log(x)/log(x^2/y). We present a new decomposition theorem
Kao, Ming-Yang +3 more
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Fullerene graphs have exponentially many perfect matchings
, 2009 A fullerene graph is a planar cubic 3-connected graph with only pentagonal and hexagonal faces.
D.J. Klein +17 more
core +1 more source
Fundamental Cycles and Graph Embeddings
, 2008 In this paper we present a new Good Characterization of maximum genus of a graph which makes a common generalization of the works of Xuong, Liu, and Fu et al.
B. Mohar +10 more
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Graceful Labeling of some Join Graphs and the Subdivision of Complete Bipartite Graphs
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.The join of graphs G and H, denoted by G + H, is the graph obtained from the disjoint union of G and H by joining each vertex in G to each vertex in H. An edge uw is said to be subdivided if uw is replaced by the path P : uvw, where v is the new vertex.
A. Panpa +3 more
wiley +1 more source
A Note on Near-factor-critical Graphs [PDF]
, 2014 A near-factor of a finite simple graph $G$ is a matching that saturates all vertices except one. A graph $G$ is said to be near-factor-critical if the deletion of any vertex from $G$ results in a subgraph that has a near-factor. We prove that a connected
Huang, Kuo-Ching, Lih, Ko-Wei
core
Graceful Labeling of Spider Graphs With at Most Five Legs
Journal of Applied Mathematics, Volume 2025, Issue 1, 2025.A graceful labeling of a graph G with q edges is an injection f from the vertices of G to the set {0, 1, ⋯, q} such that, when each edge uv is assigned the label |f(u) − f(v)|, the resulting edge labels are distinct. A spider graph is a tree with exactly one vertex of degree greater than 2, and this vertex is called the branch vertex. A leg of a spider
A. Panpa +3 more
wiley +1 more source
A polynomial-time approximation algorithm for the number of k-matchings in bipartite graphs [PDF]
, 2006 We show that the number of $k$-matching in a given undirected graph $G$ is equal to the number of perfect matching of the corresponding graph $G_k$ on an even number of vertices divided by a suitable factor.
Friedland, Shmuel, Levy, Daniel
core +1 more source