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### Contents

Games Why Study Pure Mathematics? Whats | 10 |

Introduction Sets Paradox Graphs Graph | 31 |

Recognizing Isomorphic Graphs Semantics | 56 |

Copyright | |

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### Common terms and phrases

1-platonic algebraic Chapter chromatic number closed euler walk closed hamilton walk complete graph connected graph Corollary crossing-free drawing cyclic graph Definition denoted diagrams drawn in Figure drawn without edge-crossings edge set edges of G element empty set equal erasing Euclidean geometry Euler’s Formula example Exercise expansion of UG Five Color Theorem Four Color Conjecture genus g graph G graph of Figure graph theory integer intuition Iordan Curve Theorem isomorphic graphs joined K5 is nonplanar Lemma Let G mathematical induction mathematicians multigraph nonplanar graphs null graph number of edges number of vertices odd number odd vertices one-to-one correspondence open euler walk planar and connected planar graph plane without edge-crossings platonic graph polygonal graph positive integer problem proof prove pure mathematics regular of degree second graph six vertices statement subgraph supergraph of UG surface topology true UG or K5 vertex set vertices of degree wheel graph