On the thickness and arboricity of a graph
نویسندگان
چکیده
We prove that the thickness and the arboricity of a graph with e edges are at most Lfl3 + 3/2J and r~l, respectively, and that the laller bound is best possible. The thickness of a graph G, e(G), is the mInImum number of planar graphs into which the edges of G can be partitioned, and the arboricity, J(G), is the minimum number of acyclic graphs into which the edges of G can be partitioned. Nash-Williams [9J has determined a precise formula for the arboricity of a graph; namely, All rights of reproduclion in any Corm reserved.
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 Graph Thickness, Geometric Thickness, and Separator Theorems
We investigate the relationship between geometric thickness and the thickness, outerthickness, and arboricity of graphs. In particular, we prove that all graphs with arboricity two or outerthickness two have geometric thickness O(log n). The technique used can be extended to other classes of graphs so long as a standard separator theorem exists. For example, we can apply it to show the known bo...
متن کاملMore results on r-inflated graphs: Arboricity, thickness, chromatic number and fractional chromatic number
The r-inflation of a graph G is the lexicographic product G with Kr. A graph is said to have thickness t if its edges can be partitioned into t sets, each of which induces a planar graph, and t is smallest possible. In the setting of the r-inflation of planar graphs, we investigate the generalization of Ringel’s famous Earth-Moon problem: What is the largest chromatic number of any thickness-t ...
متن کاملA pr 2 00 6 Graph Treewidth and Geometric Thickness Parameters ∗
Consider a drawing of a graph G in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of G, is the classical graph parameter thickness. By restricting the edges to be straight, we obtain the geometric thickness. By further restricting the vertices to be in convex position, we obtain the book thickness. This paper studies the relat...
متن کاملGraph Treewidth and Geometric Thickness Parameters
Consider a drawing of a graph G in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of G, is the classical graph parameter thickness. By restricting the edges to be straight, we obtain the geometric thickness. By additionally restricting the vertices to be in convex position, we obtain the book thickness. This paper studies the ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- J. Comb. Theory, Ser. B
دوره 52 شماره
صفحات -
تاریخ انتشار 1991