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Graph Theory: Level 2 Challenges

         

Can you trace this entire figure:
1) without picking up your writing/tracing tool and
2) without ever doubling back along a line already traced?

The project of building 20 roads connecting 9 cities is under way, as outlined above. So far, only some of the 20 roads are constructed, and the digit on each city indicates the number of constructed roads to other cities.

How many complete roads are there among these cities?

In the following graph, is there a path that visits each node exactly once?

You may start at any node.

Can we color the edges of the octahedron above without lifting the pencil nor coloring the same edge more than once?

Which of the following developements of the 5 platonic solids can be drawn without ever lifting the pencil from the sheet and without passing on the same edge twice?

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