## Graph theoryAlmost two decades after the appearance of most of the classical texts on the subject, this fresh introduction to graph theory offers a reassessment of the theorys main fields, methods and results today. Viewed as a branch of pure mathematics, the theory of finite graphs is developed as a coherent subject in its own right, with its own unifying questions and methods. The book thus seeks to complement, not replace, the existing more algorithmic treatments of the subject. It may be used at various different levels: it contains all the standard basic material for a first undergraduate course, complete with detailed proofs and numerous illustrations, while for a graduate course, the book offers proofs of several more advanced results. These proofs are described in as much detail as their simpler counterparts, with an informal discussion of their underlying ideas complementing their rigorous step-by-step account. Finally, for the professional mathematician the book affords an overview of graph theory as it stands today: with its typical questions and methods, its classic results, and some of those developments that have made this subject such an exciting area in recent years. |

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1-factor 3-connected adjacent Algebraic assertion average degree bijection bipartite graph called Chapter chromatic number complete graph connected graph construct contradiction Corollary cubic graph cycle in G cycle space define denote disjoint e-regular edge of G edge set edge-maximal embedding exists face of G fc-flow finite five colour theorem four colour theorem G contains G e Q(n,p given graph graph contains graph G graph theory H C G Hadwiger's conjecture Hamilton cycle hence Hint implies independent induced copy induced subgraph induction hypothesis infinite integer isomorphism least Let G maximal Menger's theorem minimal minimum degree minor theorem multigraph neighbours number of edges pair path in G perfect graph planar plane graph proof of Theorem Proposition Ramsey number Ramsey's theorem random graph regularity lemma satisfies sequence spanning trees subgraph of G subset topological minor tree-decomposition tree-width Turan's theorem Tutte's vertex set well-quasi-ordered