Graph Embedding Augmented Skill Rating System

TrueSkillTM: A Bayesian Skill Rating System

Graph Embedding

Some of the parameters used to analyze the efficiency of an embedding are dilation, expansion, edge congestion and wirelength. If e = (u, v) ∈E (G), then the length of Pf (e) in H is called the dilation of the edge e. The maximal dilation over all edges of G is called the dilation of the embedding f. The dilation of embedding G into H is the minimum dilation taken over all embeddings f of G int...

Cycle embedding of augmented cubes

A graph G 1⁄4 ðV ;EÞ is vertex-pancyclic if for every vertex u and any integer l ranging from a positive constant L to jV j, G contains a cycle C of length l such that u is in C. In this paper, we show that an n-dimensional augmented cube, where n P 2, is vertex-pancyclic with L 1⁄4 3. 2007 Elsevier Inc. All rights reserved.

Graph Embedding Using Constant Shift Embedding

In the literature, although structural representations (e.g. graph) are more powerful than feature vectors in terms of representational abilities, many robust and efficient methods for classification (unsupervised and supervised) have been developed for feature vector representations. In this paper, we propose a graph embedding technique based on the constant shift embedding which transforms a ...

On Simultaneous Graph Embedding

We consider the problem of simultaneous embedding of planar graphs. There are two variants of this problem, one in which the mapping between the vertices of the two graphs is given and another where the mapping is not given. In particular, we show that without mapping, any number of outerplanar graphs can be embedded simultaneously on an O(n)×O(n) grid, and an outerplanar and general planar gra...