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A lattice graph is a graph whose drawing, embedded in Euclidean space R2, has vertices that are the points with integer coecients, and has edges that are unit length and are parallel to the coordinate axes. A 4-regular graph is a graph where each vertex has four edges containing it; a loop containing a vertex counts as two edges. The goal for my senior project is to find upper bounds for the number of lattice edges needed to represent 4-regular graphs as lattice graphs.
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Li, Shenze, "Upper Bounds for the Number of Lattice Edges Needed to Represent 4-Regular Graphs as Lattice Graphs" (2019). Senior Projects Spring 2019. 238.
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