Table of Content s

Chapter 1. Network s 1

1.1 Countrie s o f th e insec t worl d

1.2 Notation , an d a catalog

1.3 Tree s

1.4 Tree s in graphs

1.5 Euler' s formul a

1.6 Plana r graph s

1.7 Path s i n graph s

1.8 Dua l graph s

1.9 A ma p of the Unite d State s

1.10 Colorin g graph s

1.11 Th e six-color theore m

1.12 Note s

Chapter 2 . Surface s 31

2.1 Th e shape o f the worl d

2.2 Th e fla t toru s

2.3 Graph s on th e toru s

2.4 Euler' s formula , agai n

2.5 Regula r graph s

2.6 Mor e surfaces: hole s

2.7 Mor e surfaces: connecte d sum s

2.8 One-side d surface s

2.9 Identifyin g two-side d surface s

2.10 Cel l complexe s

2.11 Note s

Chapter 3 . Knot s 5 9

3.1 Th e vie w fro m outsid e

3.2 Manipulatin g knot s

3.3 Lot s of knot s

3.4 Alternatin g knot s

3.5 Unknottin g numbe r

3.6 Link s

3.7 Linkin g numbe r

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