منابع مشابه
The linear k-arboricity of the Mycielski graph M(Kn)
A linear k-forest of an undirected graph G is a subgraph of G whose components are paths with lengths at most k. The linear k-arboricity Of G, denoted by lak(G), is the minimum number of linear k-forests needed to partition the edge set E(G) of G. In case that the lengths of paths are not restricted, we then have the linear arboricity ofG, denoted by la(G). In this paper, the exact values of th...
متن کاملThe linear 3-arboricity of Kn, n and Kn
A linear k-forest is a forest whose components are paths of length at most k. The linear k-arboricity of a graph G, denoted by lak(G), is the least number of linear k-forests needed to decompose G. In this paper, we completely determine lak(G) when G is a balanced complete bipartite graph Kn,n or a complete graph Kn, and k = 3. © 2007 Elsevier B.V. All rights reserved.
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چکیده ندارد.
15 صفحه اولLinear Arboricity and Linear k-Arboricity of Regular Graphs
We find upper bounds on the linear k-arboricity of d-regular graphs using a probabilistic argument. For small k these bounds are new. For large k they blend into the known upper bounds on the linear arboricity of regular graphs.
متن کاملMore on the linear k-arboricity of regular graphs
Bermond et al. [5] conjectured that the edge set of a cubic graph G can be partitioned into two linear k-forests, that is to say two forests whose connected components are paths of length at most k, for all k ;::: 5. That the statement is valid for all k ;::: 18 was shown in [8] by Jackson and Wormald. Here we improve this bound to k > {7 if X'( G) = 3; 9 otherwise. The result is also extended ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00365-x