## Introduction to Graph TheoryThe main objective of this work is to develop a thorough understanding of the structure of graphs and the techniques used to analyze problems in graph theory. Fundamental graph algorithms are also included. Examples and over 600 exercises - at various levels of difficulty - guide students. |

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### Contents

Fundamental Concepts | 1 |

Trees and Distance | 51 |

Matchings and Factors | 98 |

Copyright | |

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1-factor 2-connected 3-regular adjacency matrix algorithm augmenting path bipartite graph chordal graph chromatic number components compute condition connected graph construct contains cut-edge cycle of length deleting digraph disjoint dual edge-disjoint edges incident edges of G eigenvalues embedding endpoints Eulerian circuit Example Exercise G is connected graph G Hamiltonian cycle Hamiltonian path Hence hereditary system Hint implies independent set induced subgraph integers intersection interval graph isomorphic labeling least Lemma Let G lower bound matroid maximal maximum clique minimal minimum degree minimum number multigraph n-vertex graph NP-complete number of edges number of vertices obtain odd cycle pair pairwise partite set perfect graphs Petersen graph planar graph plane polynomial problem Proof Prove that G regular graph sequence simple graph simplicial spanning cycle spanning tree stable set subgraph of G subsets Suppose G Theorem tion triangle vector vertex cover vertex degrees vertex set weight y-path yields