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

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5

Connectivity and cycles

R. J. FAUDREE

1    Introduction

2    Generalizations of classical results

3    Relative lengths of paths and cycles

4    Regular graphs

5    Bipartite graphs

6    Claw-free graphs

7    Planar graphs

8    The Chvátal–Erdős condition

9    Ordered graphs

10  Numbers of cycles

References

Connectivity plays a critical role in the existence of paths and cycles in graphs. We present recent extensions of classical results on the relationship between connectivity and properties of paths, cycles and 2-factors in graphs. We also explore these connectivity-cycle relationships for special classes of graphs, such as regular, planar and claw-free graphs.

1. Introduction

Connectivity is a key graphical parameter in conditions that imply ...

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