1. Limited time only! Sign up for a free 30min personal 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!

Homework Help: Graph Theory - connection proof

  1. Sep 24, 2013 #1
    1. The problem statement, all variables and given/known data

    Prove that if a graph has > (n-1)(n-2) /2 edges, it is connected.

    2. Relevant equations


    3. The attempt at a solution

    I've drawn several examples and made tables, and I can see that the graph is indeed connected if it has more edges than [(n-1)(n-2)]/2. But what I cannot do so far is prove it. How can I start doing this proof?

  2. jcsd
  3. Sep 24, 2013 #2


    Staff: Mentor

    What does n represent here?
    How does your book define "connected" graph?
  4. Sep 24, 2013 #3
    n is the number of vertices. Connected graph means that there is no vertex that is not connected to any other by some path. Also the graph is undirected and simple (simple meaning no loops, no more than one edge between any two vertexes.)
  5. Sep 24, 2013 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You might want to do the opposite proof: if a graph is disconnected, it has fewer than or equal to (n-1)(n-2)/2 edges.

    In particular it shouldn't be hard to construct the disconnected graph with the most edges.
  6. Sep 24, 2013 #5
    That helped, thank you.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted