منابع مشابه
Almost all Regular Graphs are Hamiltonian
In a previous paper the authors showed that almost all labelled cubic graphs are hamiltonian. In the present paper, this result is used to show that almost all r-regular graphs are hamiltonian for any fixed r ≥ 3, by an analysis of the distribution of 1-factors in random regular graphs. Moreover, almost all such graphs are r-edge-colourable if they have an even number of vertices. Similarly, al...
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For all fixed trees T and any graph G we derive a counting formula for the number N̂T (G) of homomorphisms from T to G in terms of the degree sequence of G. As a consequence we obtain that any n-vertex graph G with edge density p = p(n) n−1/(t−2), which contains at most (1 + o(1))pt−1nt copies of some fixed tree T with t ≥ 3 vertices must be almost regular, i.e., ∑ v∈V (G) |deg(v)− pn| = o(pn ).
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We give a sufficient condition for a distance-regular graph to be Hamiltonian. In particular, the Petersen graph is the only connected nonHamiltonian strongly regular graph on fewer than 99 vertices.
متن کاملOn Hamiltonian Regular Graphs
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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Suppose every vertex of a graph G has degree k or k + 1 and at least one vertex has degree k + 1. It is shown that if k > 2q 2 and q is a prime power then G contains a q-regular subgraph (and hence an r-regular subgraph for all r < q. r = q (mod 2)). It is also proved that every simple graph with maximal degree A > 2q 2 and average degree d > ((2q 2)/(2q l))(A + 1), where q is a prime power, co...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1983
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(83)80039-0