Abstract. A graph is intrinsically linked if every embedding of the graph contains some pair of cycles that form a non-split link. Robertson, Seymour, and Thomas originally proved the minor-minimal set of intrinsically linked graphs to be the Petersen Family Graphs in 1995. We seek strategies

Abstract. Intrinsically linked graphs are very important spatial graphs. We say that is intrinsically knotted and 3-linked graph if every spatial embedding of this graph contains nontrivial knot and a non-split 3-component link. This paper exhibit a new intrinsically knotted and 3-linked graph

. The link of a vertex v in a graph G is the subgraph induced by all vertices adjacent to v. If all the links in G are isomorphic to the same graph L, then L is called the link graph of G. We consider the operation of an amalgamation of graphs. Using the construction of the free product of groups

A graph G is k-linked if G has at least 2k vertices, and for every sequence x1, x2,..., xk, y1, y2,..., yk of distinct vertices, G contains k vertex-disjoint paths P1, P2,..., Pk such that Pi joins xi and yi for i = 1, 2,..., k. Moreover, the above defined k-linked graph G is k-linked modulo (m1, m

The modern science of networks has brought significant advances to our understanding of complex systems. One of the most relevant features of graphs representing real systems is community structure, or clustering, i. e. the organization of vertices in clusters, with many edges joining vertices

Drawing graphs is an important problem that combines flavors of computational geometry and graph theory. Applications can be found in a variety of areas including circuit layout, network management, software engineering, and graphics. The main contributions of this paper can be summarized

A factor graph is a bipartite graph that expresses how a "global" function of many variables factors into a product of "local" functions. Factor graphs subsume many other graphical models including Bayesian networks, Markov random fields, and Tanner graphs. Following one simple

engine, special tools are required to store the link matrix of the collection of documents, due to the high number of links typically involved. This work is concerned with the application of com-pression to the link graph. We compare several techniques of compress-ing link graphs, and conclude on speed

The term Linked Data refers to a set of best practices for publishing and connecting structured data on the Web. These best practices have been adopted by an increasing number of data providers over the last three years, leading to the creation of a global data space containing billions

We present an object recognition system based on the Dynamic Link Architecture, which is an extension to classical Artificial Neural Networks. The Dynamic Link Architecture ex-ploits correlations in the fine-scale temporal structure of cellular signals in order to group neurons dynamically