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article
Some circuits in graph or network theory
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.
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problem
Doodles
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
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problem
Network trees
Explore some of the different types of network, and prove a result about network trees.
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problem
Magic caterpillars
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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problem
Tourism
If you can copy a network without lifting your pen off the paper and without drawing any line twice, then it is traversable. Decide which of these diagrams are traversable.
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problem
Maximum flow
Given the graph of a supply network and the maximum capacity for
flow in each section find the maximum flow across the network.
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problem
Production equation
Each week a company produces X units and sells p per cent of its
stock. How should the company plan its warehouse space?
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problem
Flow chart
The flow chart requires two numbers, M and N. Select several values
for M and try to establish what the flow chart does.
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problem
Zeller's birthday
What day of the week were you born on? Do you know? Here's a way to
find out.
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problem
Painting by numbers
How many different colours of paint would be needed to paint these
pictures by numbers?
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problem
Torus patterns
How many different colours would be needed to colour these
different patterns on a torus?
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problem
Drug testing
How do different drug-testing regimes affect the risks and payoffs for an athlete who chooses to take drugs?
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problem
Happy birthDay
Can you interpret this algorithm to determine the day on which you were born?
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problem
The Olympic torch tour
Imagine you had to plan the tour for the Olympic Torch. Is there an efficient way of choosing the shortest possible route?