Zsolt Tuza y Latest update : September 8, 1997 Abstract We survey the literature on those variants of the chromatic number problem where not only a proper coloring has to be found (i.e., adjacent vertices must not receive the same color) but some further local restrictions are imposed on the color assignment. Mostly, the list colorings and the precoloring extensions are considered. In one of th...

A computational approach for obtaining a similarity measure between qualitative descriptions of shape, colour and size of objects within digital images is presented. According to the definition of the qualitative features, the similarity values determined are based on conceptual neighbourhood diagrams or interval distances. An approximate matching algorithm between object descriptions is define...

Recurrent neural networks (RNNs) in combination with a pooling operator and the neighbourhood components analysis (NCA) objective function are able to detect the characterizing dynamics of sequences and embed them into a fixed-length vector space of arbitrary dimensionality. Subsequently, the resulting features are meaningful and can be used for visualization or nearest neighbour classification...

A method is proposed for obtaining the local clique set from a neighbourhood system. The Markov random field model, which is used extensively in image processing, is defined with respect to a neighbourhood system. The mathematical interpretation of the model is defined with respect to the corresponding clique set. We present a systematic method for extracting the complete local clique set from ...

A gambler moves between the vertices 1, . . . , n of a graph using the probability distribution p1, . . . , pn. Multiple cops pursue the gambler on the graph, only being able to move between adjacent vertices. We investigate the expected capture time for the gambler against k cops as a function of n and k for three versions of the game: • known gambler: the cops know the gambler’s distribution ...

In this article we present characterizations of locally well-dominated graphs and locally independent well-dominated graphs, and a sufficient condition for a graph to be k-locally independent well-dominated. Using these results we show that the irredundance number, the domination number and the independent domination number can be computed in polynomial time within several classes of graphs, e....

For a positive integer k, a k-subdominating function of G=(V; E) is a function f :V → {−1; 1} such that the sum of the function values, taken over closed neighborhoods of vertices, is at least one for at least k vertices of G. The sum of the function values taken over all vertices is called the aggregate of f and the minimum aggregate among all k-subdominating functions of G is the k-subdominat...

regarding the spatial dimension of ego/alter relations, the fact whether egos and alters live within the same neighbourhood and the consequences thereof are heavily debated. some authors argue that a network consisting mostly of people who live in the same urban area may result in lower socio-economic opportunities. another strand of research emphasizes the importance of strong ties on the loca...