[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: Proof of Wilks´ Theorem on LRT:对轻轨威尔克斯定理的证明 ...
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...
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....
Our proof in fact proves a stronger statement, which we call extended Menger's theorem, that is equivalent to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \...
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:X×X×⋯×X⏟m-times→X as T(x1,x2,…,xm)=x1+x2+⋯+xm3m, A:X→X as Ax=x2 and Fx,y(t)={tt+d(x,y),t>0,0,t=0 for ...