A good edge-labelling of a simple, finite graph is a labelling of its edges with real numbers such that, for every ordered pair of vertices (u,v), there is at most one nondecreasing path from u to v. In this paper we prove that any graph on n vertices that admits a good edge-labelling has at most n log_2(n)/2 edges, and that this bound is tight for infinitely many values of n. Thus we significantly improve on the previously best known bounds. The main tool of the proof is a combinatorial lemma which might be of independent interest. For every n we also construct an n-vertex graph that admits a good edge-labelling and has n log_2(n)/2 - O(n) edges.
A characterization of L(2, 1)-labeling number for trees with maximum degree 3
图的L（2，1）-标号是指对图G的顶点分配非负整数，使得邻顶点得到至少相差2的数，而距离为2的顶点被分配不同的数。L（2，1）-标号数就是所有这样的标号分配中最小的标号跨度值. Griggs和Yeh [Labelling graphs with a condition at distance 2，SIAM J. Discrete Math.5（1992），586-595]证明了树的L（2，1）-标号数不是\D + 1就是\D + 2。本文给出了最大度为3的树的L（2，1）-标号数的一个完全刻画.
我们研究s（k，n），A+A的最大尺寸，其中A是[n]的k-子集。加性数论中的一些已知函数可以用s（k，n）表示。例如，我们对s（k，n）的估计意味着拟Sidon集的最大大小的新界限，这是Erdos和Freud [J. Number Th.38（1991）196-205]提出的问题。此外，应用所谓的边魔术标号的图。
Trellis codes with a good distance profile constructed from expander graphs
School of Science and Engineering, The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳）理工学院）；School of Science and Engineering, Future Networks of Intelligence Institute, The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳）理工学院未来网络智能研究院）
