Transcription of Class Five: Embeddings - columbia.edu
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Class Five: Embeddings - columbia.edu
Class five : EmbeddingsK3,3K5It many applications of graph theory it is important to determine how onecan draw a particular graph with as few edges overlapping as possible. Forexample, consider the problem of designing a microchip or building a subwaysystem, overlapping edges here either lead to disfunction or are very graphis a graph which can be drawn in the plane without anyedges crossing. We refer to a specific drawing of a graph as numberof a graph is the smallest possible numberof edge crossings when considering all possible drawings of the graph. Hence,agraphisplanarifandonlyifithascros singnumberzero. Belowaretwodi erent Embeddings of the complete graph on four vertices, one with cross-ing number one and one with crossing number zero. Note, this shows thatcomplete graph on four vertices is indeed a planar graph.
Class Five: Embeddings K 3,3 K 5 It many applications of graph theory it is important to determine how one can draw a particular graph with as few edges overlapping as possible. For example, consider the problem of designing a microchip or building a subway system, overlapping edges here either lead to disfunction or are very costly.
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