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. |
Contents
Fundamental Concepts | 1 |
Trees and Distance | 51 |
Exercises | 70 |
Copyright | |
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adding adjacent algorithm appears apply assigned belongs bipartite graph bound called chromatic circuit clique closed color complete components compute condition connected consider consists construction contains copies corresponding cover crossing cycle Definition deleting Determine digraph directed disjoint distinct dual edges eigenvalues elements embedding endpoints equals exactly Example Exercise exists face flow formula function Given graph G Hamiltonian Hence holds implies incident independent set induced integers intersection labeling least Lemma length matching matrix matroid maximal maximum means minimal n-vertex neighbors obtain orientation pair partition path perfect planar graph plane points polynomial possible probability problem Proof proper Prove random regular remaining requires result satisfies sequence simple graph spanning stable set subgraph subsets sufficient Suppose Suppose G Theorem tion tree triangle union variable vertex vertex set vertices weight yields