[1] Bondy, Murty, Graph Theory, Springer, 2008 [2] Joubbeh, Minimal Separators in Graphs, 2019 [3] Youtube, Wrath of Math, Graph Theory, Proof: Menger's Theorem 编辑于 2023-11-25 00:51・IP 属地上海 图论 数学 赞同14添加评论 分享喜欢收藏申请转载 ...
a unified proof of brooks’ theorem and catlin’s theorem:一个统一的证明布鲁克斯定理和凯特林定理 热度: V12 Menger’s theorem - uni-saarlandde:的V12门格尔定理大学saarlandde 热度: A PROOF OF MENGER’S THEOREM Here is a more detailed version of the proof of Menger’s theorem on ...
Proof of Menger’s Theorem Assertion 5.3.4a If G contains a u-v path of length 2, then G contains k internally disjoint u-v paths. Proof of 5.3.4a: Suppose that P = u,e 1 ,x,e 2 ,v is a path in G of length 2. Let W be a smallest u-v separating set for the verte...
Menger's theorem states that a graph G has an (a, b)-n -fan if and only if G is n -connected between a and b . We show that G contains λ edge-disjoint (a, b)-n -fans if and only if for any k with k ≤0≤min{ n 1, | V(G) |2} and for any subset X of V(G...
There are several versions of Menger's Theorem, all can be derived from the Max-Flow-Min-Cut Theorem. Undirected, Vertex Version. LetGbe an undirected graph, and letuandvbe nonadjacent vertices inG. Then, the maximum number of pairwise-internally-disjoint(u,v)-paths inGequals the minimum nu...
Menger's Theorem for digraphs states that for any two vertex sets A and B of a digraph D such that A cannot be separated from B by a set of at most t vertices, there are t + 1 disjoint A-B-paths in D. Here a short and elementary proof of a more general theorem is given. For...
A short proof of the classical theorem of Menger concerning the number of disjoint AB-paths of a finite digraph for two subsets A and B of its vertex set i... Frank Gring - 《Discrete Mathematics》 被引量: 23发表: 2000年 On a generalization of Menger's theorem L. Lovász, V. Neumann...
The first (1) enables us to give a direct proof of Arhangel'skii's theorem [2, Theorem 6]: IfCp(X)is Menger, thenXis finite. The second (2) is an affirmative answer to Arhangel'skii's problem [5, Problem II.2.7] under CH (the continuum hypothesis)....
Then we can complete the proof by Theorem 3.1. □4 An illustration Example 4.1 Let X=[0,1], d be the usual metric on X. Define T:\underbrace{X \times X \times\cdots\times X}_{m\text{-times}}\rightarrow X as T(x_{1},x_{2},\ldots,x_{m})=\frac{x_{1}+x_{2}+...
摘要: We give necessary and sufficient regularity conditions under which the curve reconstruction problem is solved by a traveling salesman tour or path, respectively. For the proof we have to generalize a theorem of Menger [12], [13] on arc length....