Author | Bonnington, C. Paul. author |
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Title | The Foundations of Topological Graph Theory [electronic resource] / by C. Paul Bonnington, Charles H. C. Little |
Imprint | New York, NY : Springer New York, 1995 |
Connect to | http://dx.doi.org/10.1007/978-1-4612-2540-9 |
Descript | IX, 178p. 69 illus. online resource |
1 Introduction -- 1.1 Sets -- 1.2 Graphs -- 1.3 Subgraphs -- 1.4 Cocyeles -- 1.5 Forests, trees, circuits, and paths -- 1.6 Some elementary results -- 1.7 Theorems about trees -- 1.8 Spanning trees -- 1.9 Eulerian graphs -- 1.10 Bipartite graphs -- 1.11 Contractions -- 1.12 Mengerโs theorem and n-connected graphs -- 1.13 2-connected graphs -- 1.14 Blocks -- 1.15 The cycle and cocycle spaces of a graph -- 1.16 Double covers -- 2 Maps -- 2.1 Permutations -- 2.2 Maps -- 2.3 Imbeddings of maps -- 2.4 3-graphs -- 2.5 From maps to gems and back again -- 2.6 Premaps -- 3 Classification of Surfaces -- 3.1 Dipoles -- 3.2 Reduced and unitary 3-graphs -- 3.3 Canonical gems -- 3.4 Planar graphs -- 4 Consistent and Coherent Orientations -- 4.1 Orientations -- 4.2 Pairwise coherently orientable nets -- 4.3 Families of circuits -- 4.4 Rings -- 5 Non-separating Curves in Surfaces -- 5.1 The main results and their topological implications -- 5.2 Permutation pairs -- 5.3 A condition for a b-cycle to separate -- 5.4 Fundamental sets of semicycles -- 6 Mac Laneโs Theorem for 3-Graphs -- 6.1 Congruence -- 6.2 Semicycle covers -- 6.3 Boundary covers -- 6.4 Partial congruence -- 6.5 Mac Laneโs theorem -- 6.6 Whitneyโs characterisation -- 7 Kuratowskiโs Theorem -- 7.1 Corollaries of Mac Laneโs theorem -- 7.2 Kuratowskiโs theorem -- 7.3 Wagnerโs theorem -- 8 Duality -- 8.1 Duals -- 8.2 Constructing orthogonal graphs -- 8.3 Duality for planar graphs -- 8.4 The zigzag space -- 8.5 The principal edge tripartition for planar graphs -- 8.6 Walks -- 8.7 Principal cycles and principal cocycles -- 8.8 Diagonals -- 8.9 Every planar graph has a diagonal -- 8.10 No non-planar graph has a diagonal -- 9 Rings of Bonds -- 9.1 Chordal graphs -- 9.2 Rings of bonds -- 10 Bridges -- 10.1 Residues and bridges -- 10.2 Tutteโs characterisation -- List of Symbols