On the Subsets Product in Finite Groups

Let B be a proper subset of a finite group G such that either B = B−1 or G is abelian. We prove that there exists a subgroup H generated by an element of B with the following property. For every subset A of G such that A ∩ H ≠ ∅, either H ⊂ A ∪ AB or ❘A ∪ AB❘ , ❘A❘ + ❘B❘. This result generalizes the Cauchy-Davenport Theorem and two theorems of Chowla and Shepherdson

A proof of Menger's theorem by contraction

A short proof of the classical theorem of Menger concerning the number of disjoint AB-paths of a finite graph for two subsets A and B of its vertex set is given. The main idea of the proof is to contract an edge of the graph

Menger Path Systems

https://digitalcommons.memphis.edu/speccoll-faudreerj/1235/thumbnail.jp

Menger\u27s Theorem and Short Paths

https://digitalcommons.memphis.edu/speccoll-faudreerj/1228/thumbnail.jp

群ラベル付きグラフにおける組合せ最適化

学位の種別: 課程博士審査委員会委員 : （主査）東京大学教授 岩田 覚, 東京大学教授 定兼 邦彦, 東京大学教授 今井 浩, 国立情報学研究所教授 河原林 健一, 東京大学准教授 平井 広志University of Tokyo(東京大学

On Exact and Approximate Solutions for Hard Problems: An Alternative Look

We discuss in an informal, general audience style the da Costa-Doria conjecture about the independence of the P = NP hypothesis and try to briefly assess its impact on practical situations in economics. The paper concludes with a discussion of the Coppe-Cosenza procedure, which is an approximate, partly heuristic algorithm for allocation problems.P vs. NP , allocation problem, assignment problem, traveling salesman, exact solution for NP problems, approximate solutions for NP problems, undecidability, incompleteness