Eulerizing Graphs

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Example of reason to Eulerize: security guard walking the neighborhood must coverevery street block in his rounds. He wants the route with the fewest redundancies(blocks he repeats, also called deadhead blocks) that will bring him back to where hestarted.Example- 3x3 gridgraph:eulerization: now he can cover all the blocks with only 4deadheads.Important note: An eulerization should not add new vertex adjacencies. It alwaysdoubles edges.Define an OPTIMAL EULERIZATION as an eulerization that adds the fewest possibleedges.2
Example:because we can’t just connect C to B.add lots of edgesSometimes it’s simpler, even preferred, to have an Euler path in a graph instead of anEuler circuit. Just as to make the circuits, we can make an Euler path possible byadding duplicate edges, and will call this process semi-eulerization. One keyexample is in planning a parade route. We want to cover every block in our 3 by 3grid but don’t need, in fact don’t want, the parade to start and end at the same place.graph:semi-eulerize1:this semi-eulerization though has the disadvantage of the starting and ending vertex ofthe path are right next to each other. a parade is usually better off if the starting pointand ending point are far apart. How could we semi-eulerize to keep that in mind?3
Page 1: Class Notes: Eulerizing and Semi-Eu
Page 5: Add to this the additional factor o

Eulerizing Graphs

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