EC 12 (due 2/17). Prove that the dual to Eulerian planar graph is bipartite.

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EC 12 (due 2/17). Prove that the dual to
Eulerian planar graph is bipartite.
EC 13 (due 2/17). In a prison, there is a door b/w
any pair of adjacent cells and one exit guarded by
a guard G. One prisoner is a maniac M which kills
anybody he can see when he enters a cell. If M
returns to the cell with his victim, then he loses
consciousness and stops. In the evening all
inmates and the guard went to sleep in their cells.
In the morning, maniac M is gone and all other
prisoners with the guard were found dead in their
cells. Show the route of the maniac.
Transcribed Image Text:EC 12 (due 2/17). Prove that the dual to Eulerian planar graph is bipartite. EC 13 (due 2/17). In a prison, there is a door b/w any pair of adjacent cells and one exit guarded by a guard G. One prisoner is a maniac M which kills anybody he can see when he enters a cell. If M returns to the cell with his victim, then he loses consciousness and stops. In the evening all inmates and the guard went to sleep in their cells. In the morning, maniac M is gone and all other prisoners with the guard were found dead in their cells. Show the route of the maniac.
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