Cs 408 Planar Graphs Abhiram Ranade
نویسنده
چکیده
A graph is planar if it can be drawn in the plane without edges crossing. More formally, a graph is planar if it has an embedding in the plane, in which each vertex is mapped to a distinct point P (v), and edge (u, v) to simple curves connecting P (u), P (v), such that curves intersect only at their endpoints. Examples of planar graphs: Pn, Trees, Cycles, X-tree, K4. Examples of non-planar graphs: Qn for n¿3, K5, K3,3, the complete bipartite graph which each partition having 3 vertices. An important notion for planar graphs is that of a Face: which is simply a region of the plane bounded by edges of the graph. The outer infinite region is also considered a face. Planar graphs are important for several reasons. First, they are very closely linked to the early history of graph theory. Second, in the mechanical analysis of two dimensional structures, the structures get partitioned and these partitions can be represented using planar graphs. Planar graphs are also interesting because they are a large class of graphs having small separators. After studying some basic notions, we will study the colouring and separation of planar graphs.
منابع مشابه
Graphs Abhiram Ranade
A graph is planar if it can be drawn in the plane without edges crossing. More formally, a graph is planar if it has an embedding in the plane, in which each vertex is mapped to a distinct point P (v), and edge (u; v) to simple curves connecting P (u); P (v), such that curves intersect only at their endpoints. Examples of planar graphs: Pn, Trees, Cycles, X-tree, K4. Examples of non-planar grap...
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