It’s been a long since I posted something. I just started reading the marvellous book about graphs: Graph Theory by Bin Xiong,Zhongyi Zheng. There are some really good problems with solutions too and the basic theory. Graph problems are about stating the problem, fixing vertex connectivity, coloring edges/vertices and pretty much using the imagination to identify the constraints of the given conditions. The book’s chapters are: Definition of Graphs, Degree of vertex, Trees, Turin’s theorem, Euler-Hamilton graphs, Planar graphs and Ramsey applications. A nice problem with coloring:
PROBLEM: Nine mathematicians meet at an international conference and discover that among any three of them, at least two speak a common language. If each of the mathematicians speak at most three languages, prove that there are at least three of the mathematicians who can speak the same language.
For a quick view you will find it at google books. For a solution of the problem look here
zeracuse 