A Structural Property of Trees with an Application to Vertex-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...
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The vertex arboricity of graph G is the minimum number of colors that can be used to color the vertices of G so that each color class induces an acyclic subgraph of G. We prove results such as this: if a connected graph G is neither a cycle nor a clique, then there is a coloring of V(G/ with at most [-A(G)/2 ~ colors, such that each color class induces a forest and one of those induced forests ...
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The vertex arboricity a(G) of a graph G is the minimum k such that V (G) can be partitioned into k sets where each set induces a forest. For a planar graph G, it is known that a(G) ≤ 3. In two recent papers, it was proved that planar graphs without k-cycles for some k ∈ {3, 4, 5, 6, 7} have vertex arboricity at most 2. For a toroidal graph G, it is known that a(G) ≤ 4. Let us consider the follo...
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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...
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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...
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ژورنال
عنوان ژورنال: Mathematical Problems in Engineering
سال: 2017
ISSN: 1024-123X,1563-5147
DOI: 10.1155/2017/4259810