Notices
Results 1 to 3 of 3

Thread: Graph Theory Diestel Book: Question on Proposition 1.2.2

  1. #1 Graph Theory Diestel Book: Question on Proposition 1.2.2 
    New Member
    Join Date
    Jun 2011
    Posts
    2
    I am trying to teach myself graph theory. I am using Diestel's book found at http://diestel-graph-theory.com/ . Anyway, Diestel states in proposition 1.2.2:

    Every graph G with at least one edge has a subgraph H with delta(H) > epsilon(H) >= epsilon(G) .

    I am attempting to make an example but I cannot make it work. Here are my steps, can you tell me where I am wrong:

    1. Graph G has 2 vertices and 1 edge: *------*
    2. Graph H has 1 vertex: *
    3. The delta(H) = the minimum degree of G = min{d(v), where v is an element of V}
    4. I calculate the delta(H) = 0
    5. epsilon(H) = The number of edges of a H per vertex expressed as |E| / |V|.
    6. I calculate epsilon (H) = 0/1 = 0
    7. epsilon (G) = 1/2
    8. but, 0 > 0 >= 1/2 is not true.

    Where am I going wrong?

    Thanks for any help,

    Carlos


    Reply With Quote  
     

  2.  
     

  3. #2  
    Forum Freshman
    Join Date
    Aug 2010
    Posts
    97
    Graph H is identical to graph G in this case. You end up getting:

    1 > 1/2 >= 1/2


    Reply With Quote  
     

  4. #3 thanx 
    New Member
    Join Date
    Jun 2011
    Posts
    2
    thanx for the help.
    Reply With Quote  
     

Bookmarks
Bookmarks
Posting Permissions
  • You may not post new threads
  • You may not post replies
  • You may not post attachments
  • You may not edit your posts
  •