Vertex arboricity of integer distance graph G(Dm, k)
نویسندگان
چکیده
Let D be a subset of the positive integers. The distance graph G(Z,D) has all integers as its vertices and two vertices x and y are adjacent if and only if |x − y| ∈ D, where the set D is called distance set. The vertex arboricity va(G) of a graph G is the minimum number of subsets into which vertex set V(G) can be partitioned so that each subset induces an acyclic subgraph. In this paper, the vertex arboricity of graphs G(Z,Dm,k) are studied, where Dm,k = {1, 2, . . . ,m} \ {k}. In particular, va(G(Dm,1)) = dm+3 4 e for any integer m ≥ 5; va(G(Dm,2)) = d m+1 4 e+1 for m = 8l+ j ≥ 6 and j 6= 7, and d m 4 e+1 ≤ va(G(Dm,2)) ≤ d m 4 e+2 for m = 8l+ 7. © 2008 Elsevier B.V. All rights reserved.
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ورودعنوان ژورنال:
- Discrete Mathematics
دوره 309 شماره
صفحات -
تاریخ انتشار 2009