On the vertex-arboricity of planar graphs without 7-cycles
نویسندگان
چکیده
منابع مشابه
On list vertex 2-arboricity of toroidal graphs without cycles of specific length
The vertex arboricity $rho(G)$ of a graph $G$ is the minimum number of subsets into which the vertex set $V(G)$ can be partitioned so that each subset induces an acyclic graph. A graph $G$ is called list vertex $k$-arborable if for any set $L(v)$ of cardinality at least $k$ at each vertex $v$ of $G$, one can choose a color for each $v$ from its list $L(v)$ so that the subgraph induced by ev...
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 کاملA Note on Vertex Arboricity of Toroidal Graphs without 7-Cycles
The vertex arboricity ρ(G) of a graph G is the minimum number of subsets into which the vertex set V (G) can be partitioned so that each subset induces an acyclic graph. In this paper, it is shown that if G is a toroidal graph without 7-cycles, moreover, G contains no triangular and adjacent 4-cycles, then ρ(G) ≤ 2. Mathematics Subject Classification: Primary: 05C15; Secondary: 05C70
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...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2012
ISSN: 0012-365X
DOI: 10.1016/j.disc.2012.03.035