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Unformatted text preview: a, b, c, d, e as shown on the left below. Now we draw a graph 1i whose vertices are labeled a, b, c, d, e and two vertices are joined by an edge if and only if the corresponding edges cross in 91. 91 1i E@AHd n C C G b e ]1>" c B F Since 1i contains a triangle, no 2coloring exists, but there is a 2coloring of 1i . . . . {d} as shown on the left. By pulling the white edges outside the circle, 91 . . . . { d} can be redrawn as a planar graph, so removing the single adjacency constraint AG gives the hospital board a floor plan which comes as close as possible to the one desired.  n w R b W R c 91 . . . . {d} as a plane graph A H B F...
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This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.
 Summer '10
 any
 Graph Theory

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