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Extremal Problems For Transversals In Graphs With Bounded Degree

✍ Scribed by Tibor Szabó*; Gábor Tardos†

Book ID
106167595
Publisher
Springer-Verlag
Year
2006
Tongue
English
Weight
289 KB
Volume
26
Category
Article
ISSN
0209-9683

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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