On linear k-arboricity
نویسندگان
چکیده
منابع مشابه
Linear 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 کاملALGORITHMIC ASPECTS OF LINEAR k-ARBORICITY
For a fixed positive integer k, the linear k-arboricity lak(G) of a graph G is the minimum number ` such that the edge set E(G) can be partitioned into ` disjoint sets, each induces a subgraph whose components are paths of lengths at most k. This paper examines linear k-arboricity from an algorithmic point of view. In particular, we present a linear-time algorithm for determining whether a tree...
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 ...
متن کاملThe 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 کاملOn the linear arboricity of planar graphs
It is proved that the linear arboricity of every 1-planar graph with maximum degree ∆ > 33 is ⌈∆/2⌉.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1984
ISSN: 0012-365X
DOI: 10.1016/0012-365x(84)90075-x