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.
problem
Doodles
Draw a 'doodle' - a closed intersecting curve drawn without taking pencil from paper. What can you prove about the intersections?
problem
Network Trees
Explore some of the different types of network, and prove a result about network trees.
problem
Magic Caterpillars
Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.
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.
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.
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?
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.
problem
Zeller's Birthday
What day of the week were you born on? Do you know? Here's a way to
find out.
problem
Painting by Numbers
How many different colours of paint would be needed to paint these
pictures by numbers?
problem
Torus patterns
How many different colours would be needed to colour these
different patterns on a torus?
problem
Happy birthDay
Can you interpret this algorithm to determine the day on which you were born?
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?
problem
Drug testing
How do different drug-testing regimes affect the risks and payoffs for an athlete who chooses to take drugs?