Sensor networks are emerging as a paradigm for future computing, but pose a number of challenges in the fields of networking and distributed computation. One challenge is to devise a greedy routing protocol—one that routes messages through the network using only information available at a node or its neighbors. Modeling the connectivity graph of a sensor network as a 3-connected planar graph, w...

Let K be a subgraph of G, and suppose that we are given a (2-cell) embedding of K into a surface S. The embedding extension problem asks whether it is possible to extend the given embedding of K to an embedding of G in S . Every such embedding is called an embedding extension of K to G. An obstruction for embedding extensions is a subgraph 12 of G E ( K ) such that the embedding of K cannot be ...

An embedding of a graph G (into its complement * G) is a permutation on V (G) such that if an edge xy belongs to E(G) then (x) (y) does not belong to E(G). If there exists an embedding of G we say that G is embeddable or that there is a packing of two copies of the graph G into complete graph Kn. In this paper we discuss a variety of results, some quite recent, concerning the relationships betw...

We construct a graph G such that any embedding of G into R contains a nonsplit link of two components, where at least one of the components is a nontrivial knot. Further, for any m < n we produce a graph H so that every embedding of H contains a nonsplit n component link, where at least m of the components are nontrivial knots. We then turn our attention to complete graphs and show that for any...

Popular methods for speaker classification perform speaker comparison in a high-dimensional space [1], however, recent work [2] has shown that most of the speaker variability is captured by a low-dimensional subspace of that space. In this paper we examine whether additional structure in terms of nonlinear manifolds exist within the high-dimensional space. We will use graph embedding [3] as a p...

We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any reordering of the vertices. This property eliminates the difficulty of handling exponentially many isomorphic forms. Bhattacharyya kernel constructed between ...

We provide suucient conditions for packing two hypergraphs. The emphasis is on the asymptotic case when one of the hypergraphs has a bounded degree and the other is dense. As an application, we give an alternative proof for the bipartite case of the recently developed Blow-up Lemma 12].

Neural embeddings have been used with great success in Natural Language Processing (NLP). They provide compact representations that encapsulate word similarity and attain state-of-the-art performance in a range of linguistic tasks. The success of neural embeddings has prompted significant amounts of research into applications in domains other than language. One such domain is graph-structured d...

The dilation of an embedding is defined as the maximum distance between pairs of vertices of host graph that are images of adjacent vertices of guest graph. An embedding with a long dilation faces many problems, such as long communication delay, coupling problems and the existence of different types of uncontrolled noise. In this paper, we compute the minimum dilation of embedding circulant net...

The domain of graphs contains only little mathematical structure. That is, most of the basic mathematical operations, actually required by many standard computer vision and pattern recognition algorithms, are not available for graphs. One of the few mathematical concepts that has been successfully transferred from the vector space to the graph domain is distance computation between graphs, comm...