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preface to the fourth edition 1 introduction 1 what is a graph? 2 definitions and examples 2 definition 3 examples 4 three puzzles 3 paths and cycles 5 connectivity 6 eulerian graphs 7 hamiltonian graphs 8 some algorithms 4 trees 9 properties of trees 10 counting trees 11 more applications 5 planarity 12 planar graphs 13 euler's formula .14 graphs on other surfaces 15 dual graphs 16 infinite graphs 6 colouring graphs 17 colouring vertices 18 brooks' theorem 19 colouring maps 20 colouring edges 21 chromatic polynomials 7 digraphs 22 definitions 23 eulerian digraphs and tournaments 24 markov chains 8 matching, marriage and menger's theorem 25 hall's 'marriage' theorem 26 transversal theory 27 applications of hall's theorem 28 menger's theorem 29 network flows 9 matroids 30 introduction to matroids 31 examples of matroids 32 matroids and graphs 33 matroids and transversals appendix bibliography solutions to selected exercises index of symbols index of definitions |
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