1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Ramsey's theorem help~

  1. Jan 11, 2010 #1
    1. The problem statement, all variables and given/known data

    Ramsey's theorem. Let G be a graph . A clique in G is a subgraph in which every two nodes are connected by an edge . An anti-clique , also called an independent set , is a subgraph in which every two nodes are not connected by an edge . Show that every graph with n nodes contains either a clique or an anti-clique with at least 1/2log2n nodes.

    2. Relevant equations

    3. The attempt at a solution[/b

    Make space for two piles of nodes , A and B . Then , starting with the entire graph , repeatedly add each remaining node x to A if its degree is greater than one half the number of remaining nodes and to B otherwise , and discard all nodes to which x isn't(is) connected if it was added to A(B) . Continue until no nodes are left. At most half of the nodes are discarded at each of these steps , so at least log2 n steps will occur before the process terminates . Each step adds a node to one of the piles , so one of the piles ends up with at least 1/2log2 n nodes. The pile contains the nodes of a clique and the B pile contains the nodes of an anti-clique.

    I cant interpret this solution ..~ can anyone help me out..~ pls...
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?

Similar Discussions: Ramsey's theorem help~
  1. Matlab help (Replies: 0)

  2. Thermodynamics help (Replies: 0)