title: Minimum Spanning tree of a Complete Graph
body: <p>Assume <b>G = (V,E)</b> is a complete graph. </p>
  
  <p>Let the vertices be a set of points in the plane and let the edges be line segments between the points. Let the weight of each edge [a, b] be the length of the segment 'ab'.</p>
  
  <p>After reading about <b>Prim's Algorithm</b> and <b>Kruskal's Algorithm</b>, I have some sound knowledge that these greedy algorithms output the minimum spanning tree of a graph.</p>
  
  <p><b>My Question is:</b> After obtaining a minimum spanning tree of <i>G</i>, Is there a way to prove that the minimum spanning tree of <i>G</i> is a plane graph?</p>