منابع مشابه
Regular pairs in sparse random graphs I
We consider bipartite subgraphs of sparse random graphs that are regular in the sense of Szemerédi and, among other things, show that they must satisfy a certain local pseudorandom property. This property and its consequences turn out to be useful when considering embedding problems in subgraphs of sparse random graphs.
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In this paper we shall determine, when 1 = 6, bounds for numbers f(k, I) and F{k, 1) defined as follows: f{k, l)/F(k, I) is defined to be the smallest integer n for which there exists a regular graph/Hamiltonian regular graph of valency k and girth I having n vertices. The problem of determining minimal regular graphs of given girth was first considered by Tutte [9]. Bounds for f(k, I) have bee...
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Considering a connected graph G with diameter D, we say that it is k-walk-regular, for a given integer k (0 ≤ k ≤ D), if the number of walks of length l between vertices u and v only depends on the distance between them, provided that this distance does not exceed k. Thus, for k = 0, this definition coincides with that of walk-regular graph, where the number of cycles of length l rooted at a gi...
متن کاملOn 1-Arc-regular Graphs
A graph is 1-arc-regular if its full automorphism group acts regularly on the set of its arcs. In this paper, we investigate 1-arc-regular graphs of prime valency, especially of valency 3. First, we prove that if G is a soluble group then a (G, 1)-arc-regular graph must be a Cayley graph of a subgroup of G . Next we consider trivalent Cayley graphs of a finite nonabelian simple group and obtain...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1971
ISSN: 0095-8956
DOI: 10.1016/0095-8956(71)90050-5