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Some results about the interval number of a graph

✍ Scribed by Christoph Maas


Publisher
Elsevier Science
Year
1983
Tongue
English
Weight
213 KB
Volume
6
Category
Article
ISSN
0166-218X

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πŸ“œ SIMILAR VOLUMES


The total interval number of a graph
✍ T Andreae; M Aigner πŸ“‚ Article πŸ“… 1989 πŸ› Elsevier Science 🌐 English βš– 820 KB
On the Interval Number of a Triangulated
✍ Thomas Andreae πŸ“‚ Article πŸ“… 1987 πŸ› John Wiley and Sons 🌐 English βš– 414 KB πŸ‘ 2 views

The interval number of a simple undirected graph G, denoted i(G), is the least nonnegative integer r for which we can assign to each vertex in G a collection of at most r intervals on the real line such that two distinct vertices u and w of G are adjacent if and only if some interval for u intersect

On the interval number of a chordal grap
✍ Edward R. Scheinerman πŸ“‚ Article πŸ“… 1988 πŸ› John Wiley and Sons 🌐 English βš– 249 KB πŸ‘ 2 views

The interval number of a (simple, undirected) graph G is the least positive integer t such that G is the intersection graph of sets, each of which is the union of t real intervals. A chordal (or triangulated) graph is one with no induced cycles on 4 or more vertices. If G is chordal and has maximum

A note on the interval number of a graph
✍ Paul ErdΓΆs; Douglas B. West πŸ“‚ Article πŸ“… 1985 πŸ› Elsevier Science 🌐 English βš– 353 KB

Three results on the interval number of a graph on n vertices are presented. (1) The interval number of almost every graph is between n/4 Ig n and n/4 (this also holds for almost every bipartite graph). ( 2) There exist K+\_,, -free bipartite graphs with interval number at least c(m)n 1-2'Cm+1J/lg

Extremal values of the interval number o
✍ Jerrold R. Griggs πŸ“‚ Article πŸ“… 1979 πŸ› Elsevier Science 🌐 English βš– 315 KB

I i5 showll that the interval number of a gralh on n vertices is a~ inosl [I;(n ~ Ij], md this bound is best possible. This means that we can represent any l~raph ,,n n verl~cc~ as an intersection graph in which the sets ~ssigued Io the verUccs each ~or, sist of tlxe umorl ~a at m~st [~(n + I)] fini