Boxicity of Graphs on Surfaces
✍ Scribed by Louis Esperet, Gwenaël Joret
- Book ID
- 120788681
- Publisher
- Springer Japan
- Year
- 2012
- Tongue
- English
- Weight
- 223 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0911-0119
No coin nor oath required. For personal study only.
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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
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.
dedicated to professor w. t. tutte on the occasion of his eightieth birthday Let G=(V, E) be an Eulerian graph embedded on a triangulizable surface S. We show that E can be decomposed into closed curves C 1 , ..., C k such that mincr(G, D)= k i=1 mincr(C i , D) for each closed curve D on S. Here min