Cycles in graphs and problems related to matroids

在日常生活中，图形的概念已经被越来越多的应用，例如在计算机和交通网络中。在图论及其许多应用中，最重要的是循环的概念。许多算法和方法严重依赖于它的性质，为了阐明组合学的一些基本问题，还需要发现更多。举个例子，一个著名的问题被称为“旅行推销员问题”，要求人们为一个推销员找到一条“最短”的路线，从家里出发，一次访问几个城市，然后回家。在组合学中，这类问题用图中的环来建模。虽然不太可能为这样的问题找到一个“好的算法”，但对循环的研究可能会产生许多改进的方法。

In the everyday world, the concept of a graph has seen an increasing number of applications, as for example in computer and transportation networks. Of central importance to graph theory and many of its applications is the concept of a cycle. Many algorithms and methods rely heavily on its properties, and much more needs to be discovered in order to shed some light on some of the fundamental problems of combinatorics. As one example, a famous problem known as the "travelling salesman problem," asks one to find a "shortest" route for a salesman, starting from home, to visit several cities once, and return home. In combinatorics, problems of this type are modelled by cycles in a graph. While finding a "good algorithm" for a problem like this is unlikely, research on cycles may yield much improved methods.