With any (not necessarily proper) edge k-colouring γ : E(G) −→ {1, . . . , k} of a graph G, one can associate a vertex colouring σγ given by σγ(v) = ∑ e∋v γ(e). A neighbour-sumdistinguishing edge k-colouring is an edge colouring whose associated vertex colouring is proper. The neighbour-sum-distinguishing index of a graph G is then the smallest k for which G admits a neighbour-sum-distinguishin...

1 I n t r o d u c t i o n This paper investigates the problem of realizing a given graph G as a "nearest neighbour graph" of a set P of points in the plane. Roughly speaking, a "nearest neighbour graph" is a geometric graph formed from a set of points in the plane by joining two points if one is the nearest neighbour of the other. Fig. 1. A mutual nearest neighbour graph One specific kind of ne...

The paper contains a construction of a universal countable graph, different from the Rado graph, such that for any of its vertices both the neighbourhood and the non-neighbourhood induce subgraphs isomorphic to the whole graph. This solves an open problem proposed by A. Bonato; see Problem 20 in [5]. We supply a construction of several non-isomorphic graphs with the property, and consider tourn...

Abstract: Experiments in agriculture, horticulture, and forestry often show neighbour effects, that is the response on a given plot is affected by the treatments on neighbouring plot as well as by the treatment applied to that plot. When treatments are varieties, neighbour effects may be caused by differences in height, root vigor, or germination date, especially on small plots. As a result, th...

Good neighbour, bad neighbour: song sparrows retaliate against aggressive rivals Çağlar Akçay *, William E. Wood , William A. Searcy , Christopher N. Templeton , S. Elizabeth Campbell , Michael D. Beecher a,b,d Department of Psychology, University of Washington, Seattle, WA, U.S.A. Graduate Program in Neurobiology, University of Washington, Seattle, WA, U.S.A. Department of Biology, University ...

We propose a new method for the recognition of unconstrained handwritten words consisting of Korean and numeric characters. To overcome the difficulty in separating touching characters, we adopt an oversegmentation technique and we find the optimal segment combination using a lexicon-driven word scoring technique and a nearest neighbor classifier. The optimal combination gives the final segment...