Rings whose total graphs have small vertex-arboricity and arboricity
نویسندگان
چکیده
منابع مشابه
Equitable vertex arboricity of graphs
An equitable (t, k, d)-tree-coloring of a graph G is a coloring to vertices of G such that the sizes of any two color classes differ by at most one and the subgraph induced by each color class is a forest of maximum degree at most k and diameter at most d. The minimum t such that G has an equitable (t′, k, d)-tree-coloring for every t′ ≥ t is called the strong equitable (k, d)-vertex-arboricity...
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 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 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
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ژورنال
عنوان ژورنال: Hacettepe Journal of Mathematics and Statistics
سال: 2020
ISSN: 2651-477X
DOI: 10.15672/hujms.589753