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 minirmlm t for which this can be done; e
Boxicity of line graphs
β Scribed by L. Sunil Chandran; Rogers Mathew; Naveen Sivadasan
- Book ID
- 113567344
- Publisher
- Elsevier Science
- Year
- 2011
- Tongue
- English
- Weight
- 263 KB
- Volume
- 311
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
A graph has hyuiciry k if k is the smallest integer such that G is an intersection graph of k-dimensional boxes in a &-dimensional space (where the sides of the boxes are parallel to the coordinate axis). A graph has grid dimension k if k is the smallest integer such that G is an intersection graph
The intersection graph of a family 8TI of sets has the sets in %' as vertices and an edge between two sets iff they have nonempty intersection. Following Roberts [4] the boxicity b(G) of a graph G is defined as the smallest d such that G is the intersection graph of boxes in Euclidean d-space, i.e.