How to solve Euler paths & circuits.

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.