# Improved diameter bounds for altered graphs

Graphs And Geometry

First Online:

## Abstract

We consider the following problem: Given positive integers k and D, what is the maximum diameter of the graph obtained by deleting k edges from a graph G with diameter D, assuming that the resulting graph is still connected. For undirected graphs G we prove an upper bound of (k+1)D and a lower bound of (k+1)D-k for even D and of (k+1)D-2k+2 for odd D≥3. For directed graphs G, the bounds depend strongly on D: for D=1 and D=2 we derive exact bounds of θ (√k) and of 2k+2, respectively, while for D≥3 the resulting diameter is in general unbounded in terms of k and D.

## Keywords

Short Path Directed Graph Maximum Diameter Undirected Graph Diameter Increase
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## 4. References

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## Copyright information

© Springer-Verlag Berlin Heidelberg 1987