On point-linear arboricity of planar graphs
نویسندگان
چکیده
منابع مشابه
On the linear arboricity of planar graphs
It is proved that the linear arboricity of every 1-planar graph with maximum degree ∆ > 33 is ⌈∆/2⌉.
متن کاملThe List Linear Arboricity of Planar Graphs
The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. An and Wu introduce the notion of list linear arboricity lla(G) of a graph G and conjecture that lla(G) = la(G) for any graph G. We confirm that this conjecture is true for any planar graph having ∆ > 13, or for any planar graph with ∆ > 7 and without i-cycles for some i ∈ {3, 4, 5}....
متن کاملOn the Linear Arboricity of 1 - Planar Graphs ∗
It is proved that the linear arboricity of every 1-planar graph with maximum degree ∆ > 33 is ⌈∆/2⌉.
متن کاملOn the vertex-arboricity of planar graphs
The vertex-arboricity a(G) of a graph G is the minimum number of subsets into which the set of vertices of G can be partitioned so that each subset induces a forest. It is well-known that a(G) ≤ 3 for any planar graph G. In this paper we prove that a(G) ≤ 2 whenever G is planar and either G has no 4-cycles or any two triangles of G are at distance at least 3. c © 2007 Elsevier Ltd. All rights r...
متن کاملLinear 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.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1988
ISSN: 0012-365X
DOI: 10.1016/0012-365x(88)90229-4