Cubicity of interval graphs and the claw number
نویسندگان
چکیده
منابع مشابه
Cubicity of Interval Graphs and the Claw Number
Let G(V,E) be a simple, undirected graph where V is the set of vertices and E is the set of edges. A b-dimensional cube is a Cartesian product I1 × I2 × · · · × Ib, where each Ii is a closed interval of unit length on the real line. The cubicity of G, denoted by cub(G) is the minimum positive integer b such that the vertices in G can be mapped to axis parallel b-dimensional cubes in such a way ...
متن کاملOn the Cubicity of Interval Graphs
A k-cube (or “a unit cube in k dimensions”) is defined as the Cartesian product R1 × . . . × Rk where Ri(for 1 ≤ i ≤ k) is an interval of the form [ai, ai + 1] on the real line. The k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that the k-cubes mapped to two vertices in G have a non-empty intersection if and only if the vertices are adjacent. The cubicity ...
متن کاملClaw-free graphs. III. Circular interval graphs
Construct a graph as follows. Take a circle, and a collection of intervals from it, no three of which have union the entire circle; take a finite set of points V from the circle; and make a graph with vertex set V in which two vertices are adjacent if they both belong to one of the intervals. Such graphs are “circular interval graphs”, and they form an important subclass of the class of all cla...
متن کاملThe cubicity of hypercube graphs
For a graph G, its cubicity cub(G) is the minimum dimension k such that G is representable as the intersection graph of (axis– parallel) cubes in k–dimensional space. (A k–dimensional cube is a Cartesian product R1 × R2 × · · · × Rk, where Ri is a closed interval of the form [ai, ai + 1] on the real line.) Chandran et al. [2] showed that for a d–dimensional hypercube Hd, d−1 log d ≤ cub(Hd) ≤ 2...
متن کاملCubicity, Degeneracy, and Crossing Number
A k-box B = (R1, R2, . . . , Rk), where each Ri is a closed interval on the real line, is defined to be the Cartesian product R1 × R2 × · · · × Rk. If each Ri is a unit length interval, we call B a k-cube. Boxicity of a graph G, denoted as box(G), is the minimum integer k such that G is an intersection graph of k-boxes. Similarly, the cubicity of G, denoted as cub(G), is the minimum integer k s...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2010
ISSN: 0364-9024
DOI: 10.1002/jgt.20483