Results 1 to 3 of 3

Math Help - Variation of Konigsburg Bridge Problem

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    42

    Variation of Konigsburg Bridge Problem

    Is it possible to walk the seven bridges of Konigsburg so that you cross every bridge exactly twice, once in each direction? Why or why not?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Oct 2009
    Posts
    5,537
    Thanks
    778
    We can consider a directed multigraph. A simple directed graph has the following criterion: A directed graph is Eulerian iff it is strongly connected and every vertex has equal in degree and out degree. The same is probably true for a multigraph.

    In our case, the criterion is true, so I believe the answer to the original question is yes.

    A remark: To maximize chances for a helpful reply, it may be a good idea to explain some notions that are not central to the problem. In this case, one may know about Eulerian graphs but not about Königsberg.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2009
    Posts
    42
    Thank you, and yes I will explain concepts in more detail in future questions. Also, the answer to this question is yes and I was able to verify this with finding an actual path that satisfies the given conditions.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Suspension Bridge Parabola Problem
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: May 2nd 2011, 10:17 AM
  2. variation problem
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: December 9th 2010, 08:53 AM
  3. Variation problem
    Posted in the Algebra Forum
    Replies: 1
    Last Post: December 2nd 2010, 01:33 AM
  4. Parabola word problem about a suspension bridge
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: July 19th 2010, 04:35 PM
  5. Replies: 1
    Last Post: December 9th 2009, 07:00 PM

Search Tags


/mathhelpforum @mathhelpforum