Censored data, whether univariate or bivariate, and whether right{, left{ or interval cen-sored, can be represented by its intersection graph. Paying special attention to the bivariate case, we show how the maximal clique structure of such an intersection graph is related to the support of the nonparametric maximum likelihood estimate (NPMLE) of the cumulative distribution function (CDF) for su...

Graph theoretical concepts have been used to model the molecular polarizabilities of fifty-four organic derivatives, and the induced dipole moment of a set of fifty-seven organic compounds divided into three subsets. The starting point of these modeling strategies is the hydrogen-suppressed chemical graph and pseudograph of a molecule, which works very well for second row atoms. From these type...

1Research Centre of the Brain and Spinal Cord Institute, INSERM/UPMC/CNRS, 75005 Paris, France 2Department of Physiology and Pharmacology, Sapienza University of Rome, 00185 Rome, Italy 3Department of Physics and Sage Center for the Study of the Mind, University of California, Santa Barbara, CA 93106, USA 4National Laboratory of Pattern Recognition, Institute of Automation, Chinese Academy of S...

Consider the following two graphs M a n d N, both with vertex set Z×Z, where Z is the set of all integers. In M, two vertices are adjacent when their euclidean distance is 1, while in N, adjacency is obtained when the distance is either 1 or 1/2. By definition, H is a metric subgraph of the graph G if the distance between any two points o f / 4 is the same as their distance in G. We determine a...

In the present dissertation we investigate structural and algorithmic aspects of the frequency assignment problem in mobile telephone networks. This problem is of particular interest for the graph theory because of its close relationship to graph coloring. The frequency assignment problem includes the characteristic features of T-coloring, list coloring, and set coloring, and belongs thereby to...

The management of large databases of hierarchical (e.g., multi-scale or multilevel) image features is a common problem in object recognition. Such structures are often represented as trees or directed acyclic graphs (DAGs), where nodes represent image feature abstractions and arcs represent spatial relations, mappings across resolution levels, component parts, etc. Object recognition consists o...

Message authentication is considered as a serious bottleneck to multicast security, particular for stream-type of traffic. The techniques of hash chaining and signature amortization have been proposed in many schemes for stream authentication, with or without multicast settings. However, none of them is optimal. They either have a large packet overhead or are not robust to packet loss. Some eve...

We compare the notions of an end that exist in the graph-theoretical and, independently, in the topological literature. These notions conflict except for locally finite graphs, and we show how each can be expressed in the context of the other. We find that the topological ends of a graph are precisely the undominated of its graph-theoretical ends, and that graph theoretical ends have a simple t...

Over the years, several theoretical graph generation models have been proposed. Among the most prominent are: the Erdős–Renyi random graph model, Watts–Strogatz small world model, Albert–Barabási preferential attachment model, Price citation model, and many more. Often, researchers working with real-world data are interested in understanding the generative phenomena underlying their empirical g...

We characterize which systems of sign vectors are the cocircuits of an oriented matroid in terms of the cocircuit graph.