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Line 68: − Image: http://photonics.cusat.edu/images/koning4.jpg+ + + +
→Hints for difficult problems
= Hints for difficult problems =
= Hints for difficult problems =
Statement : The Königsberg bridge problem : if the seven bridges of the city of Königsberg (left figure; Kraitchik 1942), formerly in Germany but now known as Kaliningrad and part of Russia, over the river Preger can all be traversed in a single trip without doubling back, with the additional requirement that the trip ends in the same place it began. This is equivalent to asking if the multigraph on four nodes and seven edges (right figure) has an Eulerian cycle. This problem was answered in the negative by Euler (1736), and represented the beginning of graph theory.
Statement : The Königsberg bridge problem : if the seven bridges of the city of Königsberg (left figure; Kraitchik 1942), formerly in Germany but now known as Kaliningrad and part of Russia, over the river Preger can all be traversed in a single trip without doubling back, with the additional requirement that the trip ends in the same place it began. This is equivalent to asking if the multigraph on four nodes and seven edges (right figure) has an Eulerian cycle. This problem was answered in the negative by Euler (1736), and represented the beginning of graph theory.
http://photonics.cusat.edu/images/koning4.jpg
Image Courtesy : http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html
Interpretation :
= Project Ideas =
= Project Ideas =