منابع مشابه
Boxicity of series-parallel graphs
The three well-known graph classes, planar graphs(P), series-parallel graphs (SP) and outer planar graphs(OP) satisfy the following proper inclusion relation: OP ⊂ SP ⊂ P . It is known that box(G) ≤ 3 if G ∈ P and box(G) ≤ 2 if G ∈ OP . Thus it is interesting to decide whether the maximum possible value of the boxicity of series-parallel graphs is 2 or 3. In this paper we construct a series-par...
متن کاملBoxicity of line graphs
Boxicity of a graph H , denoted by box(H), is the minimum integer k such that H is an intersection graph of axis-parallel kdimensional boxes in R. In this paper, we show that for a line graph G of a multigraph, box(G) ≤ 2∆(⌈log 2 log 2 ∆⌉ + 3) + 1, where ∆ denotes the maximum degree of G. Since ∆ ≤ 2(χ−1), for any line graph G with chromatic number χ, box(G) = O(χ log 2 log 2 (χ)). For the d-di...
متن کاملBoxicity of Halin graphs
A k-dimensional box is the Cartesian product R1 × R2 × · · · ×Rk where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G) is the minimum integer k such that G is the intersection graph of a collection of k-dimensional boxes. Halin graphs are the graphs formed by taking a tree with no degree 2 vertex and then connecting its leaves to form a cycle in such ...
متن کاملPoset boxicity of graphs
A t-box representation of a graph encodes each vertex as a box in t-space determined by the (integer) coordinates of its lower and upper corner, such that vertices are adjacent if and only if the corresponding boxes intersect. The boxicity of a graph G is the minimum t for which this can be done; equivalently, it is the minimum t such that G can be expressed as the intersection graph of interva...
متن کاملBoxicity of Permutation Graphs
An axis parallel d-dimensional box is the cartesian product R1 × R2 × · · · × Rd where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G), is the minimum integer d such that G can be represented as the intersection graph of a collection of d-dimensional boxes: that is two vertices are adjacent if and only if their corresponding boxes intersect. Permutati...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2006
ISSN: 0012-365X
DOI: 10.1016/j.disc.2006.04.014