Euler's Konigsberg: the explanatory power of mathematics

The present paper provides an analysis of Euler's solutions to the Konigsberg bridges problem. Euler proposes three different solutions to the problem, addressing their strengths and weaknesses along the way. I put the analysis of Euler's paper to work in the philosophical discussion on mathematical explanations. I propose that the key ingredient to a good explanation is the degree to which it provides relevant information. Providing relevant information is based on knowledge of the structure in question, graphs in the present case. I also propose computational complexity and logical strength as measures of relevant information.