In this paper, we establish that any interval graph (resp. circulararc graph) with n vertices admits a partition into at most log 3 n (resp. log 3 n +1) proper interval subgraphs, for n>1. The proof is constructive and provides an efficient algorithm to compute such a partition. On the other hand, t
Proper interval graphs and the guard problem
β Scribed by Chiuyuan Chen; Chin-Chen Chang; Gerard J. Chang
- Book ID
- 108316104
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 437 KB
- Volume
- 170
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Given a set __F__ of digraphs, we say a graph __G__ is a __F__β__graph__ (resp., __F__\*β__graph__) if it has an orientation (resp., acyclic orientation) that has no induced subdigraphs isomorphic to any of the digraphs in __F__. It is proved that all the classes of graphs mentioned in
In this work a matrix representation that characterizes the interval and proper interval graphs is presented, which is useful for the efficient formulation and solution of optimization problems, such as the k-cluster problem. For the construction of this matrix representation every such graph is ass
## Abstract We introduce a simple new technique which allows us to solve several problems that can be formulated as seeking a suitable orientation of a given undirected graph. In particular, we use this technique to recognize and transitively orient comparability graphs, to recognize and represent
A connected graph G is a tree-clique graph if there exists a spanning tree T (a compatible tree) such that every clique of G is a subtree of T. When Tis a path the connected graph G is a proper interval graph which is usually defined as intersection graph of a family of closed intervals of the real