Why Study the Crossing Number of a Graph?
by David Wood
Abstract: The crossing number of a given graph is the minimum number of crossings in a drawing of that graph. This seminar will be a broad introduction to this topic, aimed at an audience with little or no background in graph theory. I will describe the history of the crossing number, applications of the crossing number to other areas of mathematics, such as combinatorial geometry (the Szemeredi- Trotter theorem) and combinatorial number theory (sum-sets and product- sets), as well as applications in computer science (network visualisation). I will conclude the talk by discussing my own research that establishes connections between the crossing number and structural graph theory (graph minors).
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