Abstract
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. c © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 79–84, 1997
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