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question 1 the graph gl at left in figure is planar how many faces does a planar drawing of gl have2 the graph gr at
question 1 prove that the graph shown in figure is non-planar2 the girth of a graph is the length of its smallest
question 1 attempt to embed k5 on the torus is it possible2 attempt to embed k5 on the mumlobius band is it possible3
question 1 for which mn is kmn planar and for which mn is kmn non planar make and prove a conjecture2 check out figure
question 1 prove that for a planar graph with k components vg-egfg 1k2 prove that the petersen graph shown in figure
question theorem requires that g have no 3-cycles this requirement could be replaced with the constraint that g be
question draw a non-simple graph that violates theoremtheorem if g is simple planar and connected then g has at least
question why is the constraint vg ge 3 necessary in theoremtheorem if g is simple planar and connected and has at least
question 1 go to httpplanaritynet enjoy2 verify eulers formula for k4 be sure to draw k4 without edges crossing3 draw
question 1 find three new planar drawings of the right-hand graph of figure 112 what are the face sizes for each
question 1 find two different planar drawings of the left-hand graph of figure each of which has a face of size 6 how
question use the results of the previous problem to generalize the statements and proofs of theorems i and iitheorem i
question 1 compute the thickness of k332 compute the thickness of the petersen graph3 give an example of a 4-regular
question generalize theorem slightly prove that every simple planar connected graph g has at least three vertices of
question 1 might the graph in figure be planar2 the goal of this problem is to use eulers formula to list all possible
question 1 write a story proof of eulers formula involving ducks2 prove that the graph shown in figure is non-planar3
question 1 prove that if g has 11 vertices and is simple then g and gmacr cannot both be planar2 can you find a graph
question 1 draw six different graphs each with a different number of vertices check to see whether each graph has an
question 1 conjecture a necessary condition for a graph to have an euler circuit ie if a graph has an euler circuit
question find a minimum-weight spanning tree of the graph given in example first use any method you like then do it
question 1 now suppose that the information given in the previous problem is listed in preference order ie the book the
question 1 consider the mini-sudoku puzzle of figure 1024 in which each row column and quadrant needs to contain the
question 1 make a standard drawing of k33 do you think there is a different drawing of k33 with no edges crossing2 is
question after example we examine the case of a class on the reality of ducks below are listed the students and the
question 1 show that a graph is connected if and only if it has a spanning tree2 how many different binary search trees