Embedding Graphs into Embedded Graphs

Embedding Graphs into Embedded Graphs

A drawing of a graph G in the plane is weakly simple if it can be turned into an embedding by an arbitrarily small perturbation. We show that testing, whether a straight-line drawing of a planar graph G in the plane is weakly simple, can be carried out in polynomial time, if a desired embedding of G belongs to a fixed isotopy class. In other words, we show that c-planarity with pipes is tractab...

Embedding Cartesian Products of Graphs into De Bruijn Graphs Embedding Cartesian Products of Graphs into De Bruijn Graphs

(m 2) of nontrivial connected graphs G i and the n-dimensional base B de Bruijn graph D = D B (n), we investigate whether or not there exists a spanning subgraph of D which is isomorphic to G. We show that G is never a spanning subgraph of D when n is greater than three or when n equals three and m is greater than two. For n = 3 and m = 2, we can show for wide classes of graphs that G cannot be...

Simultaneous Embedding of Embedded Planar Graphs

Given k planar graphs G1,...,Gk, deciding whether they admit a simultaneous embedding with fixed edges (SEFE) and whether they admit a simultaneous geometric embedding (SGE) are NP-hard problems, for k ≥ 3 and for k ≥ 2, respectively. In this talk we consider the complexity of the SEFE problem and of the SGE problem when graphs G1,...,Gk have a fixed planar embedding. In sharp contrast with the...

An Embedding of Existential Graphs into Concept Graphs with Negations

Embedding arbitrary finite simple graphs into small strongly regular graphs

It is well-known that any nite simple graph ? is an induced sub-graph of some exponentially larger strongly regular graph ? (e.g. 2, 8]). No general polynomial-size construction has been known. For a given-nite simple graph ? on v vertices we present a construction of a strongly regular graph ? on O(v 4) vertices that contains ? as its induced sub-graph. A discussion is included of the size of ...