Scientists, engineers, and educators commonly need to make graphs that quickly illustrate quantitative ideas yet are not based on specific data sets. We call these graphs quantita...
We give an O(n log n) algorithm for computing the girth (shortest cycle) of an undirected n-vertex planar graph. Our solution extends to any graph of bounded genus. This improves u...
We solve the subgraph isomorphism problem in planar graphs in linear time, for any pattern of constant size. Our results are based on a technique of partitioning the planar graph ...
Steinitz’s Theorem states that a graph is the 1-skeleton of a convex polyhedron if and only if it is 3-connected and planar. The polyhedron is called a geometric realization of ...
Dan Archdeacon, C. Paul Bonnington, Joanna A. Elli...
ABSTRACT. Upon the discovery of power laws [8, 16, 30], a large body of work in complex network analysis has focused on developing generative models of graphs which mimick real-wor...