The search for N-e.c. graphs
نویسنده
چکیده
Almost all finite graphs have the n-e.c. adjacency property, although until recently few explicit examples of such graphs were known. We survey some recently discovered families of explicit finite n-e.c. graphs, and present a new construction of strongly regular n-e.c. arising from affine planes.
منابع مشابه
On an adjacency property of almost all graphs
A graph is called n-existentially closed or n-e.c. if it satis/es the following adjacency property: for every n-element subset S of the vertices, and for every subset T of S, there is a vertex not in S which is joined to all of T and to none of S\T . The unique countable random graph is known to be n-e.c. for all n. Equivalently, for any /xed n, almost all /nite graphs are n-e.c. However, few e...
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We give new examples of graphs with the n-e.c. adjacency property. Few explicit families of n-e.c. graphs are known, despite the fact that almost all nite graphs are n-e.c. Our examples are collinearity graphs of certain partial planes derived from a¢ ne planes of even order. We use probabilistic and geometric techniques to construct new examples of n-e.c. graphs from partial planes for all n,...
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Random graphs with high probability satisfy the n-e.c. adjacency property, although until recently few explicit examples of such graphs were known. We supply a new general construction for generating infinite familes of finite regular n-e.c. graphs derived from certain resolvable Steiner 2-designs. We supply an extension of our construction to the infinite case, and thereby give a new represent...
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A graph is n-e.c. (n-existentially closed) if for every pair of subsets A,B of vertex set V of the graph such that A∩B = ∅ and |A|+ |B| = n, there is a vertex z not in A∪B joined to each vertex of A and no vertex of B. Few explicit families of n-e.c. are known for n > 2. In this short note, we give a new construction of 3-e.c. graphs using the notion of quadrance in the finite Euclidean space Zdp.
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ورودعنوان ژورنال:
- Contributions to Discrete Mathematics
دوره 4 شماره
صفحات -
تاریخ انتشار 2009