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8

Toughness and binding numbers

1   Introduction

2   Toughness and connectivity

3   Toughness and cycles

4   Toughness and k-factors

5   Binding number

6   Binding number and k-factors

7   Binding numbers and cycles

8   Other measures of vulnerability

References

The toughness and binding number of a graph are two measures of how its edges are distributed and how well the graph is connected. We survey the main properties of toughness and binding number, and study the conditions upon them that ensure the existence of factors and cycles.

1. Introduction

The concept of toughness was introduced by Václav Chvátal [21] in 1973. As he wrote, toughness ‘measures in a simple way how tightly various pieces of graph hold together’.

The origin ...

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