## We characterize those interval graphs G with the property that, for every vertex u, there exists an interval represention of G in which the interval representing 21 is the left-most (or right-most) interval in the representation.
On the homogeneous representation of interval graphs
β Scribed by Stephan Olariu
- Publisher
- John Wiley and Sons
- Year
- 1991
- Tongue
- English
- Weight
- 705 KB
- Volume
- 15
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
β¦ Synopsis
Abstract
An interval graph G is homogeneously representable if for every vertex v of G there exists an interval representation of G with v corresponding to an end interval. We show that the homogeneous representation of interval graphs is rooted in a deeper property of a class of graphs that we characterize by forbidden configurations.
π SIMILAR VOLUMES
## Abstract The interval number of a graph __G__ is the least natural number __t__ such that __G__ is the intersection graph of sets, each of which is the union of at most __t__ intervals, denoted by __i__(__G__). Griggs and West showed that $i(G)\le \lceil {1\over 2} (d+1)\rceil $. We describe the
Let x(G) and o(G) denote the chromatic number and clique number of a graph G. We prove that x can be bounded by a function of o for two well-known relatives of interval graphs. Multiple interval graphs (the intersection graphs of sets which can be written as the union of t closed intervals of a line