Introduction to Graph TheoryPrentice Hall, 1996 - 512 ˹éÒ The 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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Fundamental Concepts | 1 |
Trees and Distance | 51 |
Spanning Trees in Graphs | 65 |
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2-connected 3-regular a₁ adjacency matrix adjacent algorithm bipartite graph chordal graph chromatic number components compute condition connected graph construct contains cycle matroid cycle of length d₁ deleting digraph disjoint dual edge-disjoint edges incident edges of G eigenvalues embedding endpoints Eulerian circuit Example Exercise G₁ graph G Hamiltonian cycle Hamiltonian path Hence hereditary system Hint implies independent set induced subgraph integer intersection interval graph isomorphic k-coloring k-critical labeling Lemma lower bound matching matrix matroid maximal maximum clique Menger's Theorem minimal minimum number n-vertex graph NP-complete number of edges number of vertices obtain odd cycle pair pairwise path perfect graphs Petersen graph planar graph plane polynomial problem Proof Prove that G regular graphs sequence simple graph simplicial spanning cycle spanning tree stable set subgraph of G subsets Suppose G Theorem tion triangle u₁ v₁ variable vectors vertex degrees vertex set x₁ y-path yields