This is not possible. "A continuous line without overlapping sections" for the figure constitutes a eulerian cycle (http://en.wikipedia.org/wiki/Eulerian_cycle). A necessary condition for eulerian cycles is that all vertices should have even degree.

A cycle is not required to draw the figure. It is a eulerian trail, not cycle. From wikipedia: "An undirected graph has an Eulerian trail if and only if at most two vertices have odd degree, and if all of its vertices with nonzero degree belong to a single connected component." so this problem has a solution.

you start from the right down corner going up to the right upper corner,then to top corner,after to the left upper corner,then to the down right corner,after to the down left corner, then to the upper right corner,after to the left upper corner and you finish to the down left corner

This is not possible. "A continuous line without overlapping sections" for the figure constitutes a eulerian cycle (http://en.wikipedia.org/wiki/Eulerian_cycle). A necessary condition for eulerian cycles is that all vertices should have even degree.

ReplyDeleteI solve it! CORRECT?

ReplyDeletehttps://word.office.live.com/wv/WordView.aspx?FBsrc=https%3A%2F%2Fwww.facebook.com%2Fdownload%2Ffile_preview.php%3Fid%3D542684365782742%26time%3D1366577248%26metadata&access_token=100003495100230%3AAVKFoyUGpQ6msRT9j3KTvNQtBSHS4etURXB_DswUXIFovw&title=KUCICA.doc

A cycle is not required to draw the figure. It is a eulerian trail, not cycle. From wikipedia: "An undirected graph has an Eulerian trail if and only if at most two vertices have odd degree, and if all of its vertices with nonzero degree belong to a single connected component." so this problem has a solution.

ReplyDeleteso my solution is RIGHT???

ReplyDeleteyou start from the right down corner going up to the right upper corner,then to top corner,after to the left upper corner,then to the down right corner,after to the down left corner, then to the upper right corner,after to the left upper corner and you finish to the down left corner

ReplyDeleteΠανεύκολακι.....

ReplyDeleteΠανεύκολο

ReplyDelete