✦ LIBER ✦

Homogeneously representable interval graphs

✍ Scribed by Dale Skrien; John Gimbel

Publisher: Elsevier Science
Year: 1985
Tongue: English
Weight: 258 KB
Volume: 55
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(85)90049-4

No coin nor oath required. For personal study only.

✦ Synopsis

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.

📜 SIMILAR VOLUMES

On the homogeneous representation of int

On the homogeneous representation of interval graphs

✍ Stephan Olariu 📂 Article 📅 1991 🏛 John Wiley and Sons 🌐 English ⚖ 705 KB

## 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 clas

Interval representations of planar graph

Interval representations of planar graphs

✍ Carsten Thomassen 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 867 KB

Open-interval graphs versus closed-inter

Open-interval graphs versus closed-interval graphs

✍ P. Frankl; H. Maehara 📂 Article 📅 1987 🏛 Elsevier Science 🌐 English ⚖ 218 KB

A graph G = (V, E) is said to be represented by a family F of nonempty sets if there is a bijection f:V--\*F such that uv ~E if and only iff(u)Nf(v)q=~. It is proved that if G is a countable graph then G can be represented by open intervals on the real line if and only if G can be represented by clo

Interval graphs and interval orders

✍ Peter C. Fishburn 📂 Article 📅 1985 🏛 Elsevier Science 🌐 English ⚖ 949 KB

This paper explores the intimate connection between finite interval graphs and interval orders. Special attention is given to the family of interval orders that agree with, or provide representations of, an interval graph. Two characterizations (one by P. Hanlon) of interval graphs with essentially

Lexicographic orientation and representa

Lexicographic orientation and representation algorithms for comparability graphs, proper circular arc graphs, and proper interval graphs

✍ Pavon Hell; Jing Huang 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 823 KB

## 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

Random interval graphs

✍ Nicholas Pippenger 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 209 KB 👁 1 views

We consider models for random interval graphs that are based on stochastic service systems, with vertices corresponding to customers and edges corresponding to pairs of customers that are in the system simultaneously. The number N of vertices in a connected component thus corresponds to the number o