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Total interval number for graphs with bounded degree

✍ Scribed by Kostochka, Alexander V.; West, Douglas B.

Publisher: John Wiley and Sons
Year: 1997
Tongue: English
Weight: 90 KB
Volume: 25
Category: Article
ISSN: 0364-9024
DOI: 10.1002/(sici)1097-0118(199705)25:1<79::aid-jgt5>3.0.co;2-f

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✦ Synopsis

The total interval number of an n-vertex graph with maximum degree ∆ is at most (∆+1/∆)n/2, with equality if and only if every component of the graph is K ∆,∆ . If the graph is also required to be connected, then the maximum is ∆n/2 + 1 when ∆ is even, but when ∆ is odd it exceeds [∆ + 1/(2.5∆ + 7.7)]n/2 for infinitely many n.

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