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In 2012, the head of AP Grading, Trevor Packer, stated that the reason for the low percentages of 5s is that "AP World History is a college-level course, & many sophomores aren't yet writing at that level." 10.44 percent of all seniors who took the exam in 2012 received a 5, while just 6.62 percent of sophomores received a 5.
The induced width of an ordered graph is the width of its induced graph. [2] Given an ordered graph, its induced graph is another ordered graph obtained by joining some pairs of nodes that are both parents of another node. In particular, nodes are considered in turn according to the ordering, from last to first. For each node, if two of its ...
The design may have inspired later 'Maps of World History' such as the HistoMap by John B. Sparks, which chronicles four thousand years of world history in a graphic way similar to the enlarging and contracting nation streams presented on Adam's chart. Sparks added the innovation of using a logarithmic scale for the presentation of history.
A graph formed from a given graph by deleting one vertex, especially in the context of the reconstruction conjecture. See also deck, the multiset of all cards of a graph. carving width Carving width is a notion of graph width analogous to branchwidth, but using hierarchical clusterings of vertices instead of hierarchical clusterings of edges.
The width of a graph is an alternative name for the degeneracy of the graph - the smallest k for which every subgraph has a vertex of degree at most k. Bandwidth of a graph - the minimum, over all orderings of vertices of G, of the length of the longest edge (the number of steps in the ordering between its two endpoints).
A 3-map graph is a planar graph, and every planar graph can be represented as a 3-map graph. Every 4-map graph is a 1-planar graph , a graph that can be drawn with at most one crossing per edge, and every optimal 1-planar graph (a graph formed from a planar quadrangulation by adding two crossing diagonals to every quadrilateral face) is a 4-map ...
In graph theory, the graph bandwidth problem is to label the n vertices v i of a graph G with distinct integers so that the quantity {| () |:} is minimized (E is the edge set of G). [1] The problem may be visualized as placing the vertices of a graph at distinct integer points along the x -axis so that the length of the longest edge is ...
The carving width is only one of several graph width parameters that measure how tree-like a given graph is. Others include the treewidth and branchwidth.The branchwidth of a graph is defined similarly to carving width, using hierarchical clusterings, but of the edges of a graph rather than of its vertices; these are called branch-decompositions.