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Mathematics is an exciting and accessible activity for many who only think of mathematics in terms of formulas and numbers. How would you like to discover new mathematical results? Impossible you say – perhaps not. In EXCURSION VI we learn about a result published in a major journal of graph theory which was discovered by a Professor of French Literature. This result had stumped more than one professional mathematician. Not everyone who studies these EXCURSIONS will be aiming at making an original research contribution, however everyone who undertakes these EXCURSIONS seriously should gain an insight into the problems of graph theory.
For too long mathematicians have been content to talk about their work only with other mathematicians. These EXCURSIONS give a wider audience the opportunity to take part in a dynamic creative process in the area of graph theory. The basic tools needed to understand current efforts in graph theory are accessible to interested and inquisitive readers – regardless of their previous mathematical training. After becoming familiar with the basic terminology which is found in EXCURSION I, the Reader should feel free to pursue the other EXCURSIONS in any order. In fact, the Reader should feel free to return at a future time to any of the EXCURSIONS without having to relearn the notions of graph theory. The reason for this is very simple. Most terminology in graph theory is merely a formal description of what is usually a very natural notion.
Euler graphs.
Ringel's problem.
Dancing children.
Hamiltonian cycles.
Triple systems.
Embeddings of graphs.
Chromatic polynomials