منابع مشابه
Regular subgraphs of almost regular graphs
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...
متن کاملThree-regular Subgraphs of Four-regular Graphs'
The Berge–Sauer conjecture (see [2, 3]) says that any simple (no multiple edges and loops) 4-regular graph contains a 3-regular subgraph. This conjecture was proved in [4, 6]. In [1, 2] the Chevalley–Warning theorem was used to extend this result to graphs with multiple edges, which are 4-regular plus an edge. Our main result, Theorem 2.2, presents the sufficient condition for a 4-regular graph...
متن کاملRegular subgraphs of random graphs
In this paper, we prove that there exists a function ρk = (4 + o(1))k such that G(n, ρ/n) contains a k-regular graph with high probability whenever ρ > ρk. In the case of k = 3, it is also shown that G(n, ρ/n) contains a 3-regular graph with high probability whenever ρ > λ ≈ 5.1494. These are the first constant bounds on the average degree in G(n, p) for the existence of a k-regular subgraph. W...
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For integers a and b, 0 ≤ a ≤ b, an [a, b]-graph G satisfies a ≤ deg(x,G) ≤ b for every vertex x of G, and an [a, b]-factor is a spanning subgraph F such that a ≤ deg(x, F ) ≤ b for every vertex x of F . An [a, b]-factor is almost-regular if b = a+1. A graph is [a, b]-factorable if its edges can be decomposed into [a, b]-factors. When both k and t are positive integers and s is a nonnegative in...
متن کاملOn almost distance-regular graphs
Distance-regular graphs have been a key concept in Algebraic Combinatorics and have given place to several generalizations, such as association schemes. Motivated by spectral and other algebraic characterizations of distance-regular graphs, we study ‘almost distance-regular graphs’. We use this name informally for graphs that share some regularity properties that are related to distance in the ...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1984
ISSN: 0095-8956
DOI: 10.1016/0095-8956(84)90047-9