McKee, T.A., Intersection properties of graphs, Discrete Mathematics 89 (1991) 253-260. For each graph-theoretic property, we define a corresponding 'intersection property', motivated by the natural relationship of paths with interval graphs, and of trees with chordal graphs. We then develop a simp
Intersection graphs of halflines and halfplanes
✍ Scribed by Sandi Klavžar; Marko Petkovšek
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 318 KB
- Volume
- 66
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Intersection graphs of segments (the class SEG) and of other simple geometric objects in the plane are considered. The results fall into two main areas: how difficult is the membership problem for a given class and how large are the pictures needed to draw the representations. Among others, we prove
Let G and H be two graphs of order n. If we place copies of G and H on a common vertex set, how much or little can they be made to overlap? The aim of this article is to provide some answers to this question, and to pose a number of related problems. Along the way, we solve a conjecture of Erd" os,
For an arbitrary graph G we determine the asymptotics of the intersection number (edgeclique covering number) of the categorical (or weak) product of G and the complete graph K,, asymptotically in n. The result follows from a more general theorem on graph capacities which generalizes an earlier resu
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
A graph is an intersection graph if it is possible to assign sets to its vertices so that adjacency corresponds exactly to nonempty intersection. If the sets assigned to vertices must belong to a pre-specified family, the resulting class of all possible intersection graphs is called an intersection