4.3 二分图中的匹配和覆盖 Matchings & coverings in bipartite graphs 在这个部分,我们专注于二分图中的匹配问题。 令G = (A, B, E) 表示一个二分图 我们称一组节点集合 U 为G 的节点覆盖(vertex cover)若每条 G 的边都被 U 中的一个节点覆盖(覆盖指的就是,若一个节点是一条边的端点,那么我们就...
In Section 3.2, we obtain an analogous result for the set BG2(n,γ) of connected bipartite graphs with n vertices and γ cut edges. The unique greatest element with respect to ⪯ is the same as the one in BG1(n,γ) (namely BPn,γ). As an immediate consequence, this graph maximizes...
A graph is bipartite if its set of points V(G) can be partitioned into two sets, A and B, such that every line in E(G) has one endpoint in A and the other in B. The sets A and B are often called the color classes of G and (A, B) a bipartition of G. The chapter ...
The present paper shows how to construct a maximum matching in a bipartite graph with n vertices and m edges in a number of computation steps proportional to (m + n)x/. Key words, algorithm, algorithmic analysis, bipartite graphs, computational complexity, graphs, matching 1. Introduction. Sup...
{n^2\\\ln^3 n}{d}\\\}) expected time algorithm for finding a perfect matching in regular bipartite graphs; as a function of n n alone, the a... A Goel,M Kapralov,S Khanna - 《Stoc Proceedings of Acm Symposium on Theory of Computing》 被引量: 57发表: 2009年 Distributed-Memory...
We present an algorithm for finding a large matching in a bipartite graph in the semi-streaming model. In this model, the input graph G = (V, E) is represented as a stream of its edges in some arbitrary order, and storage of the algorithm is bounde
in t w o disjoin t sets V = A _ [ B and all edges on tain v erti es from b oth sets, i.e. E � A � B . A graph is regular if all v erti es ha v e the same degree. W e will only onsider bipartite graphs with jAj = jB j and will denote jAj b y n, impli...
Let {E1, . . . , Em} be a partition of E(Kn,n), where Kn,n is the complete bipartite graph, and assume that ∣Ei∣/n ∈ Z. It was conjectured in [1], that there exists a perfect matching M in Kn,n withs(M) = max i (∣M ∩ Ei ∣ ? ∣Ei ∣/n)– min i (∣M...
This result is consistent with the polynomial solvability of the C k -free 2-matching problem in bipartite graphs and partially proves the conjecture of Cunningham that the degree sequences of C 4 -free 2-matchings form a jump system for any graph. We also show that the weighted square-...
In this paper we show that, with 11 exceptions, any matching covered bipartite graph on n vertices, with minimum degree greater than two, has at least 2n-4 perfect matchings. Using this bound, which is the best possible, and McCuaig's theorem [W. McCuaig, J. Graph Theory, 38 (2001...