In my very early ages, I have planned to set up a personal blog. However, all my personal blogs were discarded either because I felt tired to maintain it or I felt nobody was going to read my posts. And as you see, this is my another attempt, and I would try my best to maintain this blog for this ti

Problem definition An undirected graph is -coloring if all vertices could be colored with at most different colors, such that all adjacent vertices have different colors. For example, a -clique is -coloring, and a tree is 2-coloring. The densest subgraph of a graph , is an induced subgraph of a vert

A tree is a connected undirected graph with nodes and edges. The diameter of a tree is the largest distance between two nodes in the tree. We define a growing tree as follows: at each moment, a new node is inserted into the tree, and is connected to some node in the original tree. What is the diame

In this article, we would use to represent the bitwise XOR operation between two integers. We observe that: for any , , and therefore, for any . We now illustrate the formal proof of the above observation. We firstly write into a binary format, i.e.: Let . Then: Then the binary formats