منابع مشابه
The Logic of Random Regular Graphs
The first order language of graphs is a formal language in which one can express many properties of graphs — known as first order properties. The classic Zero-One law for random graphs states that if p is some constant probability then for every first order property the limiting probability of the binomial random graph G(n, p) having this property is either zero or one. The case of sparse rando...
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In a previous paper we showed that a random 4-regular graph asymptotically almost surely (a.a.s.) has chromatic number 3. Here we extend the method to show that a random 6-regular graph asymptotically almost surely (a.a.s.) has chromatic number 4 and that the chromatic number of a random d-regular graph for other d between 5 and 10 inclusive is a.a.s. restricted to a range of two integer values...
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The family of random regular graphs is a classic topic in the realms of graph theory, combinatorics and computer science. In this paper we study the problem of learning random regular graphs from random paths. A random regular graph is generated uniformly at random and in a standard label-guided graph exploration setting, the edges incident from a node in the graph have distinct local labels. T...
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Strongly regular graphs lie on the cusp between highly structured and unstructured. For example, there is a unique strongly regular graph with parameters (36,10,4,2), but there are 32548 non-isomorphic graphs with parameters (36,15,6,6). (The first assertion is a special case of a theorem of Shrikhande, while the second is the result of a computer search by McKay and Spence.) In the light of th...
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ژورنال
عنوان ژورنال: Journal of Combinatorics
سال: 2010
ISSN: 2156-3527,2150-959X
DOI: 10.4310/joc.2010.v1.n4.a3