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

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6

H-linked graphs

MICHAEL FERRARA and RONALD J. GOULD

1   Introduction

2   k-linked graphs

3   Weak linkage

4   Digraphs

5   Modulo and parity linkage

6   Disjoint connected subgraphs

7   The disjoint paths problem

8   H-linked graphs

9   H-extendible graphs

References

Given graphs G and H, we say that G is H-linked provided that every injective function f : V (H) → V (G) can be extended to a subdivision of H. When H = kK2, this is the well-known k-linked problem. In this chapter we trace the development of H-linked graphs and consider a number of natural variations of the problem.

1. Introduction

One of the most natural and central properties in the study of graphs is connectivity. Connectivity is so important that many variants of how a graph ...

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