Abstract
The total interval number of an n-vertex graph with maximum degree Δ is at most (Δ + 1/Δ)n/2, with equality if and only if every component of the graph is KΔ,Δ. If the graph is also required to be connected, then the maximum is Δn/2 + 1 when Δ is even, but when Δ is odd it exceeds [Δ + 1/(2.5Δ + 7.7)]n/2 for infinitely many n. © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 79–84, 1997
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