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A complete graph with n nodes represents the edges of an (n – 1)-simplex. Geometrically K 3 forms the edge set of a triangle, K 4 a tetrahedron, etc. The Császár polyhedron, a nonconvex polyhedron with the topology of a torus, has the complete graph K 7 as its skeleton. [15] Every neighborly polytope in four or more dimensions also has a ...
K 6 is at the top of the illustration, K 3,3,1 is in the upper right, and the Petersen graph is at the bottom. The blue links indicate ΔY- or YΔ-transforms between graphs in the family. In graph theory, the Petersen family is a set of seven undirected graphs that includes the Petersen graph and the complete graph K 6.
A maximal outerplanar graph and its 3-coloring The complete graph K 4 is the smallest planar graph that is not outerplanar.. In graph theory, an outerplanar graph is a graph that has a planar drawing for which all vertices belong to the outer face of the drawing.
The seven 3-connected cubic well-covered graphs are the complete graph K 4, the graphs of the triangular prism and the pentagonal prism, the Dürer graph, the utility graph K 3,3, an eight-vertex graph obtained from the utility graph by a Y-Δ transform, and the 14-vertex generalized Petersen graph G(7,2). [18]
(That is, any graph of treewidth > k includes one of the graphs in the set as a minor.) Each of these sets of forbidden minors includes at least one planar graph. For k = 1, the unique forbidden minor is a 3-vertex cycle graph. [5] For k = 2, the unique forbidden minor is the 4-vertex complete graph K 4. [5]
English: Gray, blue, red, green, light green, black graph papers with 1 cm–0.5 cm–1 mm grids (page size: A4) in printable PDF format. Date 25 July 2013, 18:04:17