منابع مشابه
On 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 کاملEeciently Computing Vertex Arboricity of Planar Graphs
Acyclic-coloring of a graph G = (V; E) is a partitioning of V , such that the induced subgraph of each partition is acyclic. The minimum number of such partitions of V is deened as the vertex arboricity of G. An O(n) algorithm (n = jV j) for acyclic-coloring of planar graphs with 3 colors is presented. Next, an O(n 2) heuristic is proposed which produces a valid acyclic-2-coloring of a planar g...
متن کاملEÆciently Computing Vertex Arboricity of Planar Graphs
Acyclic-coloring of a graph G = (V;E) is a partitioning of V , such that the induced subgraph of each partition is acyclic. The minimumnumber of such partitions of V is de ned as the vertex arboricity of G. An O(n) algorithm (n = jV j) for acyclic-coloring of planar graphs with 3 colors is presented. Next, an O(n) heuristic is proposed which produces a valid acyclic-2-coloring of a planar graph...
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⌉.
متن کاملEquitable vertex arboricity of planar graphs
Let G1 be a planar graph such that all cycles of length at most 4 are independent and let G2 be a planar graph without 3-cycles and adjacent 4-cycles. It is proved that the set of vertices of G1 and G2 can be equitably partitioned into t subsets for every t ≥ 3 so that each subset induces a forest. These results partially confirm a conjecture of Wu, Zhang
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2007
ISSN: 0012-365X
DOI: 10.1016/j.disc.2005.12.055