11. Find a Hamilton path in the graph below and prove that no Hamilton circuit exists.abcnopedfgjlkmhi(6)
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12. Use the circle-chord method to determine whether the following graph is planar. If it is, give a planardrawing. It if is not, find aK3,3- orK5-configuration.bacjikfegdh(8)
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(See example 4, section 1.4 (Tucker)andStudy Guide p.15 & 16).We use the Hamilton circuitabefghckjida. By inside-outside symmetry we choose the edgeafto bedrawn inside. Then the edgebchas to be drawn outside. Now the edgedecannot be drawn inside oroutside. (Find edges in such a way that the previous choices force the next edge to be drawn inonlyone possible way.)Hence the graph is not planar:becghjiafkdThe following is aK3,3configuration of the graph,aecfdbkighj10