ScholarLens Back to search
1988•Journal of Graph TheoryRequires access

On the interval number of a chordal graph

Edward R. Scheinerman

Open publisher page 4 citations

Abstract

Abstract 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 clique size ω(G) = m, then i(G) ⩽ [1 + o(1)]m/log2 m and this result is best possible, even for split graphs (chordal graphs whose complement is also chordal).

About this research paper

What this paper is about

Abstract 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 clique size ω(G) = m, then i(G) ⩽ [1 + o(1)]m/log2 m and this result is best possible, even for split graphs (chordal graphs whose complement is also chordal).

Why it matters

OpenAlex reports 4 citations for this work. Citation counts describe recorded attention and do not establish research quality.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Abstract 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 clique size ω(G) = m, then i(G) ⩽ [1 + o(1)]m/log2 m and this result is best possible, even for split graphs (chordal graphs whose complement is also chordal).

Key concepts: Chordal graph, Interval graph, Combinatorics, Mathematics, Split graph, Block graph, Discrete mathematics, Outerplanar graph

Related papers

Related paper 1Related paper 2
Back to paper searchBrowse research topicsOriginal source
On the interval number of a chordal graph — Research Paper | ScholarLens