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How to solve Euler paths & circuits.

How to solve Euler paths & circuits. by Mr. King. First – let’s review…. What is a Euler circuit? What is a Euler path? Tell someone next to you what you remember. Euler Circuits. Euler circuits follow these rules: All vertices are equal .

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How to solve Euler paths & circuits.

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  1. How to solve Euler paths & circuits. by Mr. King

  2. First – let’s review… • What is a Euler circuit? • What is a Euler path? Tell someone next to you what you remember.

  3. Euler Circuits • Euler circuits follow these rules: • All vertices are equal. • You can trace a pencil over every edge without retracing any edges or lifting your pencil, and… • You start and finish at the same vertex.

  4. Euler Paths • Euler paths follow these rules: • The graph has 2 odd vertices. • You can trace a pencil over every edge without retracing or lifting your pencil, but… • You will start and finish at different vertices.

  5. Back to solving… • You probably noticed that solving Euler paths and circuits can be messy and confusing. When you trace with a pencil, you may end up with this-

  6. Use a system instead! • Instead of scribbling all over your paper, use symbols and make a system. • Mark your starting point, then use symbols to mark your progress. • Try using: / X O ~ • Use colors:/XO~

  7. Use a system instead! • Instead of scribbling all over your paper, use symbols and make a system. • Mark your starting point, then use symbols to mark your progress. • Try using: / X O ~ • Use colors:/XO~

  8. Use a system instead! • Instead of scribbling all over your paper, use symbols and make a system. • Mark your starting point, then use symbols to mark your progress. • Try using: / X O ~ • Use colors:/XO~

  9. Use a system instead! • Instead of scribbling all over your paper, use symbols and make a system. • Mark your starting point, then use symbols to mark your progress. • Try using: / X O ~ • Use colors:/XO~

  10. Use a system instead! • Instead of scribbling all over your paper, use symbols and make a system. • Mark your starting point, then use symbols to mark your progress. • Try using: / X O ~ • Use colors:/XO~

  11. Use a system instead! • Instead of scribbling all over your paper, use symbols and make a system. • Mark your starting point, then use symbols to mark your progress. • Try using: / X O ~ • Use colors:/XO~

  12. Switch symbols when you fail, and label your vertices to mark your progress

  13. Switch symbols when you fail, and label your vertices to mark your progress

  14. Switch symbols when you fail, and label your vertices to mark your progress

  15. Switch symbols when you fail, and label your vertices to mark your progress

  16. Switch symbols when you fail, and label your vertices to mark your progress

  17. Switch symbols when you fail, and label your vertices to mark your progress

  18. Switch symbols when you fail, and label your vertices to mark your progress

  19. Switch symbols when you fail, and label your vertices to mark your progress

  20. Switch symbols when you fail, and label your vertices to mark your progress

  21. Switch symbols when you fail, and label your vertices to mark your progress

  22. Switch symbols when you fail, and label your vertices to mark your progress

  23. Switch symbols when you fail, and label your vertices to mark your progress

  24. Switch symbols when you fail, and label your vertices to mark your progress

  25. Switch symbols when you fail, and label your vertices to mark your progress

  26. Switch symbols when you fail, and label your vertices to mark your progress

  27. Switch symbols when you fail, and label your vertices to mark your progress

  28. Switch symbols when you fail, and label your vertices to mark your progress

  29. Switch symbols when you fail, and label your vertices to mark your progress

  30. Switch symbols when you fail, and label your vertices to mark your progress

  31. Switch symbols when you fail, and label your vertices to mark your progress

  32. Switch symbols when you fail, and label your vertices to mark your progress

  33. Switch symbols when you fail, and label your vertices to mark your progress

  34. Switch symbols when you fail, and label your vertices to mark your progress

  35. Switch symbols when you fail, and label your vertices to mark your progress

  36. Switch symbols when you fail, and label your vertices to mark your progress

  37. Switch symbols when you fail, and label your vertices to mark your progress

  38. Switch symbols when you fail, and label your vertices to mark your progress

  39. Switch symbols when you fail, and label your vertices to mark your progress

  40. Try it yourself- • Label your vertices, • Choose a vertex to start at, • Use a symbol or color to mark your route, • Write out the route as you go.

  41. You can also solve backwards. • Check each route by following it. • Use your symbols to mark the route. • Remember the rules for circuits and paths: • Circuits start and end at the same vertex. • Paths start and end at different vertices. • You have to go over every edge only once without lifting your pencil.

  42. You can also solve backwards. • Check each route by following it. • Use your symbols to mark the route. • Remember the rules for circuits and paths: • Circuits start and end at the same vertex. • Paths start and end at different vertices. • You have to go over every edge only once without lifting your pencil.

  43. You can also solve backwards. • Check each route by following it. • Use your symbols to mark the route. • Remember the rules for circuits and paths: • Circuits start and end at the same vertex. • Paths start and end at different vertices. • You have to go over every edge only once without lifting your pencil.

  44. You can also solve backwards. • Check each route by following it. • Use your symbols to mark the route. • Remember the rules for circuits and paths: • Circuits start and end at the same vertex. • Paths start and end at different vertices. • You have to go over every edge only once without lifting your pencil.

  45. You can also solve backwards. • Check each route by following it. • Use your symbols to mark the route. • Remember the rules for circuits and paths: • Circuits start and end at the same vertex. • Paths start and end at different vertices. • You have to go over every edge only once without lifting your pencil.

  46. You can also solve backwards. • Check each route by following it. • Use your symbols to mark the route. • Remember the rules for circuits and paths: • Circuits start and end at the same vertex. • Paths start and end at different vertices. • You have to go over every edge only once without lifting your pencil.

  47. You can also solve backwards. • Check each route by following it. • Use your symbols to mark the route. • Remember the rules for circuits and paths: • Circuits start and end at the same vertex. • Paths start and end at different vertices. • You have to go over every edge only once without lifting your pencil.

  48. You can also solve backwards. • Did you notice what was wrong with route #1? • Tell someone sitting next to you why route #1 was neither a Euler path or circuit.

  49. You can also solve backwards. • Route #1 never covered the A-C edge. • Let’s try route #2. • Don’t forget to use a different symbol or color!

  50. You can also solve backwards. • Route #1 never covered the A-C edge. • Let’s try route #2.

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