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21.
G. Tinhofer 《Annals of Operations Research》1984,1(3):239-254
This paper deals with the expected cardinality of greedy matchings in random graphs. Different versions of the greedy heuristic for the cardinality matching problem are considered. Experimental data and some theoretical results are reported. 相似文献
22.
Let be a tree. We show that the null space of the adjacency matrix of has relevant information about the structure of . We introduce the Null Decomposition of trees, which is a decomposition into two different types of trees: N-trees and S-trees. N-trees are the trees that have a unique maximum (perfect) matching. S-trees are the trees with a unique maximum independent set. We obtain formulas for the independence number and the matching number of a tree using this decomposition. We also show how the number of maximum matchings and the number of maximum independent sets in a tree are related to its null decomposition. 相似文献
23.
G. Mazzuoccolo 《Discrete Mathematics》2013,313(20):2292-2296
24.
25.
We construct highly edge-connected -regular graphs of even order which do not contain pairwise disjoint perfect matchings. When is a multiple of 4, the result solves a problem of Thomassen [4]. 相似文献
26.
The matching graph M(G) of a graph G is that graph whose vertices are the maximum matchings in G and where two vertices M1 and M2 of M(G) are adjacent if and only if |M1 − M2| = 1. When M(G) is connected, this graph models a metric space whose metric is defined on the set of maximum matchings in G. Which graphs are matching graphs of some graph is not known in general. We determine several forbidden induced subgraphs of matching graphs and add even cycles to the list of known matching graphs. In another direction, we study the behavior of sequences of iterated matching graphs. © 1998 John Wiley & Sons, Inc. J. Graph Theory 29: 73–86, 1998 相似文献
27.
Anush Tserunyan 《Discrete Mathematics》2009,309(4):693-1613
For a given graph consider a pair of disjoint matchings the union of which contains as many edges as possible. Furthermore, consider the ratio of the cardinalities of a maximum matching and the largest matching in those pairs. It is known that for any graph is the tight upper bound for this ratio. We characterize the class of graphs for which it is precisely . Our characterization implies that these graphs contain a spanning subgraph, every connected component of which is the minimal graph of this class. 相似文献
28.
A minimal blocker in a bipartite graph G is a minimal set of edges the removal of which leaves no perfect matching in G. We give an explicit characterization of the minimal blockers of a bipartite graph G. This result allows us to obtain a polynomial delay algorithm for finding all minimal blockers of a given bipartite graph. Equivalently, we obtain a polynomial delay algorithm for listing the anti‐vertices of the perfect matching polytope of G. We also provide generation algorithms for other related problems, including d‐factors in bipartite graphs, and perfect 2‐matchings in general graphs. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 209–232, 2006 相似文献
29.
We consider a family of generalized matching problems called k-feasible matching (k-RM) problems, where k? {1,2,3,…} ∪ {∞}. We show each k-FM problem to be NP-complete even for very restricted cases. We develop a dynamic programming algorithm that solves in polynomial time the k-FM problem for graphs with width bounded by 2k. We also show that for any subset S of {1,2,…} ∪ {∞}, there is a set D of problem instances such that for k in S the k-FM problem is NP-complete on D, while for k not in S the k-FM problem is polynomially solvable on D. 相似文献
30.
A rainbow matching for (not necessarily distinct) sets of hypergraph edges is a matching consisting of k edges, one from each . The aim of the article is twofold—to put order in the multitude of conjectures that relate to this concept (some first presented here), and to prove partial results on one of the central conjectures. 相似文献