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Extremal Values of the Interval Number of a Graph

✍ Scribed by Griggs, Jerrold R.; West, Douglas B.

Book ID: 118212352
Publisher: Society for Industrial and Applied Mathematics
Year: 1980
Weight: 792 KB
Volume: 1
Category: Article
ISSN: 0196-5212
DOI: 10.1137/0601001

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📜 SIMILAR VOLUMES

Extremal values of the interval number o

Extremal values of the interval number of a graph, II

✍ Jerrold R. Griggs 📂 Article 📅 1979 🏛 Elsevier Science 🌐 English ⚖ 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

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The total interval number of a graph

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✍ Thomas Andreae 📂 Article 📅 1988 🏛 Elsevier Science 🌐 English ⚖ 552 KB

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✍ Thomas Andreae 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 414 KB 👁 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

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✍ Edward R. Scheinerman 📂 Article 📅 1988 🏛 John Wiley and Sons 🌐 English ⚖ 249 KB 👁 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