Planar Graphs · Planar Separators (Optional)

Lesson 3

Nikolai Chukhin · Alexander S. Kulikov

Problem. Mark all correct statements. Assume that \(G\) is already drawn on the plane, and \(G^{*}\) is the dual graph of this drawing.

1 point

  1. The graph \(G^{*}\) has exactly one edge for every edge of \(G\).

  2. If \(G\) is simple, then \(G^{*}\) must also be simple.

  3. If an edge of \(G\) has the same face on both sides, then its dual edge is a loop.

  4. If \(G\) is a tree, then \(G^{*}\) has one vertex and all its edges are loops.