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Topics in Structural Graph Theory by Ortrud R. Oellermann, Robin J. Wilson, Lowell W. Beineke

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2

Maximally connected graphs

DIRK MEIERLING and LUTZ VOLKMANN

1   Introduction

2   Maximally edge-connected graphs

3   Maximally edge-connected digraphs

4   Maximally locally edge-connected graphs and digraphs

5  Maximally connected and maximally locally connected graphs and digraphs

6   Restricted edge-connectivity

7   Conditional vertex-connectivity and edge-connectivity

References

That the edge-connectivity of a graph does not exceed the minimum degree of a vertex in the graph follows at once from the definitions. A graph is called maximally edge-connected if equality holds, and in this chapter, we explore conditions on a graph that guarantee that it is maximally edge-connected. Similarly, a graph is called maximally connected if its connectivity ...

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