General properties of some families of graphs defined by systems of equations
General properties of some families of graphs defined by systems of equations
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DOI：
10.1002/jgt.1024
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发表时间：
2001-10
影响因子：
0.9
通讯作者：
F. Lazebnik;A. Woldar
中科院分区：
文献类型：
--
作者：
F. Lazebnik;A. Woldar
在本文中，我们提出了一种简单的方法，用于构建由一类方程式在交换环上定义的无限族。覆盖地图的存在（因此，嵌入了光谱）是同一家族的每两个成员之间。以这种方式构造的边缘构造的跨度或完整的两部分均在许多情况下，这些构造的专业是在各种图理论问题中有用的。包括结果。 Sons，Inc。J图理论38：65-86，2001
In this paper we present a simple method for constructing infinite families of graphs defined by a class of systems of equations over commutative rings. We show that the graphs in all such families possess some general properties including regularity and biregularity, existence of special vertex colorings, and existence of covering maps—hence, embedded spectra—between every two members of the same family. Another general property, recently discovered, is that nearly every graph constructed in this manner edge‐decomposes either the complete, or complete bipartite, graph which it spans. In many instances, specializations of these constructions have proved useful in various graph theory problems, but especially in many extremal problems. A short survey of the related results is included. We also show that the edge‐decomposition property allows one to improve existing lower bounds for some multicolor Ramsey numbers. © 2001 John Wiley & Sons, Inc. J Graph Theory 38: 65–86, 2001