The Petersen Graph (Australian Mathematical Society Lecture Series, Series Number 7)

The Petersen Graph Occupies An Important Position In The Development Of Several Areas Of Modern Graph Theory Because It Often Appears As A Counter-example To Important Conjectures. In This Account, The Authors Examine Those Areas, Using The Prominent Role Of The Petersen Graph As A Unifying Feature. Topics Covered Include: Vertex And Edge Colourability (including Snarks), Factors, Flows, Projective Geometry, Cages, Hypohamiltonian Graphs, And 'symmetry' Properties Such As Distance Transitivity. The Final Chapter Contains A Pot-pourri Of Other Topics In Which The Petersen Graph Has Played Its Part. Undergraduate Students Will Be Able To Profit From Reading This Book As The Prerequisites Are Few; Thus It Could Be Used For A Second Course In Graph Theory. On The Other Hand, The Authors Have Also Included A Number Of Unsolved Problems As Well As Topics Of Recent Study. Thus It Will Also Be Useful As A Reference For Graph Theorists. 1. The Petersen Graph -- 2. Regular Graphs And Connectivity -- 3. Bipartite Graphs -- 4. Automorphism Groups -- 5. Hamiltonian Graphs -- 6. Planar Graphs -- 7. Graph Colourings -- 2. The Four Colour Problem -- 1. The Five Colour Theorem -- 2. Unavoidable Configurations -- 3. Reducible Configurations -- 4. The Four Colour Theorem -- 5. Hadwiger And Hajos -- 6. Tait's Method -- 3. Snarks -- 1. Vizing's Theorem -- 2. Isaacs' Snarks -- 3. K-snarks(k > 3) -- 4. Factors -- 1. Tait's Conjecture -- 2. Tutte's Characterization -- 3. Petersen's Graph -- 4. Factor-covered -- 5. F-factors -- 6. Applications -- 5. Beyond The Four Colour Theorem -- 1. Flows -- 2. A Result Of Seymour -- 3. Projective Geometry -- 4. Colourings And Projective Spaces -- 6. Cages -- 2. Upper Bounds For F(r,g) -- 3. Small Cages -- 4. Symmetry And Cages -- 7. Hypohamiltonian Graphs -- 1. Sousselier's Problem -- 2. Petersen Generalizations -- 8. Symmetry -- 1. Distance Transitive Graphs -- 2. Distance Transitive Line Graphs -- 3. Rank 3 Graphs -- 4. Strongly Regular Graphs -- 5. Homogeneous Graphs -- 9. The Petersen Graph In Diversity -- 1. The Dodecahedron And P -- 2. Locally Petersen Graphs -- 3. Spectral Properties Of P -- 4. Orientations -- 5. Hamiltonian Paths And The Petersen Graph -- 6. Kneser's Conjecture -- 7. Odd Graphs -- 8. The Johnson Graphs And Even Graphs -- 9. Embeddings -- 10. The Cycle Double Cover Conjecture -- 11. Geodetics -- 12. Geodetics And An Extremal Problem -- 13. Generalized Petersen And Permutation Graphs -- 14. Generalized Petersen Edge-colourings And Groups -- 15. Pandora's Box. D.a. Holton, J. Sheehan. Includes Bibliographical References And Index.