图的不变量与大圈--纯链目录
Graph Invariants and Large Cycles - a Catalog of Pure Links
摘要：
图的不变量为研究图的抽象结构提供了一个强有力的分析工具。它们以方便的关系结合在一起，携带着关于图及其各种子结构的全局和一般信息，如圈结构、因子、匹配、着色、覆盖等，这些子结构的发现是图论的首要问题。本文的主要目的是列出图的基本不变式与图的大圈结构（Hamilton圈、最长圈和控制圈）之间的所有纯关系及其推广。基本图不变量和纯关系允许专注于没有先行者的结果。这些最简单的“祖先”形成了一个源泉，几乎所有可能的哈密顿结果都可以通过各种额外的新思想、推广、扩展、限制和结构限制得到进一步的发展，同时也帮助研究人员对该领域“复杂”的发展机制做出清晰而简单的想象。
英文摘要：
Graph invariants provide a powerful analytical tool for investigation of abstract structures of graphs. They, combined in convenient relations, carry global and general information about a graph and its various substructures such as cycle structures, factors, matchings, colorings, coverings, and so on, whose discovery is the primary problem of graph theory. The major goal of this paper is to catalogue all pure relations between basic invariants of a graph and its large cycle structures, namely Hamilton, longest and dominating cycles and some their generalizations. Basic graph invariants and pure relations allow to focus on results having no forerunners. These simplest kind of "ancestors" form a source from which nearly all possible hamiltonian results can be developed further by various additional new ideas, generalizations, extensions, restrictions and structural limitations, as well as helping researchers to make clear and simple imagination about "complicated" developmental mechanisms in the area.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
