Cycles in graphs and problems related to matroids

在日常生活中，图的概念有越来越多的应用，例如在计算机和交通网络中。 对于图论及其许多应用来说，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，并且需要发现更多的东西，以便揭示组合学的一些基本问题。 作为一个例子，一个著名的问题被称为“旅行推销员问题”，要求一个推销员找到一条“最短”路线，从家开始，访问几个城市一次，然后返回家。 在组合数学中，这类问题是用图中的圈来建模的。 虽然为这样的问题找到一个“好算法”是不太可能的，但对循环的研究可能会产生更好的方法。

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.