In a graph G, the distance from an edge e to a set F ⊆ E(G) is the vertex distance from e to F in the line graph L(G). For a decomposition of E(G) into k sets, the distance vector of e is the k-tuple of distances from e to these sets. The decomposition dimension dec(G) of G is the smallest k such that G has a decomposition into k sets so that the distance vectors of the edges are distinct. For ...

The vertices of the odd-distance graph are the points of the plane R. Two points are connected by an edge if their Euclidean distance is an odd integer. We prove that the chromatic number of this graph is at least five. We also prove that the odd-distance graph in R is countably choosable, while such a graph in R is not.

Results of stellar evolution calculations and results of non-adiabatic stellar pulsation calculations can be used to construct theoretical , composition-dependent, short period boundaries (or \blue edges") of the instability strip in the period-luminosity plane for Cepheids pulsating in the fundamental and rst overtone radial modes. The slopes of these blue edges are very similar to the slopes ...

The distance preserving graph embedding problem is to embed vertices of a given weighted graph into points in d-dimensional Euclidean space for a constant d so that for each edge the distance between their corresponding endpoints is as close to the weight of the edge as possible. If the given graph is complete, that is, if distance constraints are given as a full matrix, then multi-dimensional ...

The distance preserving graph embedding problem is to embed vertices of a given weighted graph into points in 2-dimensional Euclidean space so that for each edge the distance between their corresponding endpoints is as close to the weight of the edge as possible. If the given graph is complete, that is, if distance constraints are given as a full matrix, then principal coordinate analysis can s...

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[1] Entrainment processes in convective clouds often occur stochastically and entrainment rate estimates depend on the distance from the cloud from which the dry air is entrained. However, no observational studies exist on either the distance dependence or probability density function of entrainment rate, hindering understanding and the parameterization of convection. Here entrainment rate in c...

For a graph property P, the edit distance of a graph G from P, denoted EP(G), is the minimum number of edge modifications (additions or deletions) one needs to apply to G in order to turn it into a graph satisfying P. What is the furthest graph on n vertices from P and what is the largest possible edit distance from P? Denote this maximal distance by ed(n,P). This question is motivated by algor...

Using natural nests of eight bird species, we provide one of the first multispecies tests for edge effects on reproductive success in a forested landscape. Our primary objective was to assess whether distance to the edge of recent clearcuts was related to nesting success in intact northern hardwood forests. Estimated nest success was generally lower for the two ground-nesting species than for t...