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12euler_10

# 12euler_10 - 1 ENGG1007 FCS 1 ENGG1007 Foundations of...

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Unformatted text preview: 1 ENGG1007 FCS 1 ENGG1007 Foundations of Computer Science Click to edit Master subtitle style Euler Path/Circuit Prof. Francis Chin, Dr SM Yiu November 8/10, 2010 (Chapter 9) 2 ENGG1007 FCS Knigsbergs Bridge Problem Can we cross all bridges once and return to the starting point? (circuit) Is there a circuit containing every edge in this graph? Equivalent problem : Can you draw this graph without lifting the pen from paper or repeating any lines (edges)? What about a path which visits all bridges without returning to the starting point? Modeling the problem in terms of graphs: 3 ENGG1007 FCS Euler Paths and Circuits An Euler circuit (or cycle) is a simple circuit containing every edge in the graph. An Euler path is a simple path containing every edge in the graph. Example: How to determine whether a graph has an Euler path/circuit? 4 ENGG1007 FCS Some other Graphs 5 ENGG1007 FCS Existence of Euler Paths/Circuits Some observations: Connectivity?...
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12euler_10 - 1 ENGG1007 FCS 1 ENGG1007 Foundations of...

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