Theory of finite and infinite graphs
Theory of finite and infinite graphs
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DOI：
10.1007/978-1-4684-8971-2_2
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发表时间：
1990
期刊：
影响因子：
--
通讯作者：
D. König
中科院分区：
文献类型：
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作者：
D. König
前言图论可以从两个不同的角度来理解。首先，像理论的一维复合物，它形成的第一部分一般拓扑结构。其次，如果从它的连续几何内容中抽象出来，它可以被认为是组合学和抽象集合论的一个分支。这本书采取第二种观点，主要是因为我们不认为图的元素，点和边，任何几何内容：点（顶点）是任意可区分的元素，而边只不过是它的两个端点的集合。西尔维斯特（1873）强调的这个抽象概念，除了几个例子和应用之外，在我们的介绍中将严格遵守。我们仍然使用的几何符号给出了一个非常方便的术语，而没有假设任何几何观点或几何公理。这个图论术语有很大的启发价值：它概括了”自然”问题，并将相当抽象的事物与清晰的概念联系起来，由此，似乎彼此遥远的概念和问题之间的新联系经常出现。这种抽象的组合概念也有利于几何拓扑学，正如多维组合（庞加莱-凡勃伦）拓扑学最近经历的巨大发展所示。当然，复杂和流形的一个以上的层面上的避免”连续”是连接更大的困难。出于这个原因，我们限制自己，为了保持这本书的相当基本的性质，绝对图论，它认为图形本身，而
Foreword Graph theory can be conceived from two different standpoints. First, like the theory of one dimensional complexes, it forms the first part of general topology. Secondly, it can be conceived, if one abstracts from its continuous-geometrical content, as a branch of combinatorics and abstract set theory. This book takes the second standpoint mainly because we do not ascribe to the elements of graphs, points and edges, any geometrical content at all: the points (vertices) are arbitrary distinguishable elements, and an edge is nothing other than a collection of its two endpoints. This abstract conception, which Sylvester emphasized (1873), will be strictly adhered to in our presentation, with the exception of several examples and applications. The geometrical notation, which we nevertheless use, gives a very convenient terminology without assuming any geometrical view or geometrical axioms. This graph theoretical terminology has a great heuristic value: it furnishes" natural" problems and connects quite abstract things with clear ideas, whereby new connections among concepts and problems seemingly distant from one another often come to light. Also this abstract-combinatorial conception is of advantage for geometrical topology, as is shown by the great development that multidimensional combinatorial (Poincare-Veblen) topology has experienced in recent times. Certainly for complexes and manifolds of more than one dimension the avoidance of the" continuous" is connected with greater difficulties. For this reason we restrict ourselves, in order to preserve the quite elementary character of this book, to absolute graph theory, which considers graphs in themselves, while