Graph theory / Reinhard Diestel.
Idioma: Inglés Lenguaje original: Alemán Series Graduate texts in mathematics ; 173Editor: New York : Springer, c1997Descripción: xiv, 286 p. ; 24 cmISBN: 0387982116 (pbk.); 0387982108Títulos uniformes: Graphentheorie. Inglés Otra clasificación: 05-011. The Basics [1] 1.1. Graphs [2] 1.2. The degree of a vertex [4] 1.3. Paths and cycles [6] 1.4. Connectivity [9] 1.5. Trees and forests [12] 1.6. Bipartite graphs [13] 1.7. Contraction and minors [15] 1.8. Euler tours [17] 1.9. Some linear algebra [19] 1.10. Other notions of graphs [23] Exercises [25] Notes [26] 2. Matching [29] 2.1. Matching in bipartite graphs [29] 2.2. Matching in general graphs [84] 2.3. Path covers [38] Exercises Notes [42] 3. Connectivity [43] 3.1. 2-Connected graphs and subgraphs [43] 3.2. The structure of 3-connected graphs [45] 3.3. Menger’s theorem [50] 3.4. Mader’s theorem [55] 3.5. Edge-disjoint spanning trees [57] 3.6. Paths between given pairs of vertices [60] Exercises [62] Notes [64] 4. Planar Graphs [67] 4.1. Topological prerequisites [68] 4.2. Plane graphs [70] 4.3. Drawings [77] 4.4. Planar graphs: Kuratowski’s theorem [81] 4.5. Algebraic planarity criteria [85] 4.6. Plane duality [87] Exercises [90] Notes [92] 5. Colouring [95] 5.1. Colouring maps and planar graphs [96] 5.2. Colouring vertices [98] 5.3. Colouring edges [103] 5.4. List colouring [105] 5.5. Perfect graphs [110] Exercises [117] Notes [121] 6. Flows [123] 6.1. Circulations [124] 6.2. Flows in networks [125] 6.3. Group-valued flows [128] 6.4. k-Flows for small k [133] 6.5. Flow-colouring duality [136] 6.6. Tutte’s flow conjectures [140] Exercises [144] Notes [146] 7. Substructures in Dense Graphs [147] 7.1. Subgraphs [148] 7.2. Szemerédi’s regularity lemma [153] 7.3. Applying the regularity lemma [160] Exercises [165] Notes [166] 8. Substructures in Sparse Graphs [169] 8.1. Topological minors [170] 8.2. Minors [178] 8.3. Hadwiger’s conjecture [180] Exercises [184] Notes [185] 9. Ramsey Theory for Graphs [187] 9.1. Ramsey’s original theorems [188] 9.2. Ramsey numbers [191] 9.3. Induced Ramsey theorems [194] 9.4. Ramsey properties and connectivity [205] Exercises [206] Notes [208] 10. Hamilton Cycles [211] 10.1. Simple sufficient conditions [211] 10.2. Hamilton cycles and degree sequences [214] 10.3. Hamilton cycles in the square of a graph [216] Exercises [224] Notes [226] 11. Random Graphs [227] 11.1. The notion of a random graph [228] 11.2. The probabilistic method [233] 11.3. Properties of almost all graphs [236] 11.4. Threshold functions and second moments [240] Exercises [245] Notes [247] 12. Minors, Trees, and WQO [249] 12.1. Well-quasi-ordering [249] 12.2. The minor theorem for trees [251] 12.3. Tree-decompositions [253] 12.4. Tree-width and forbidden minors [257] 12.5. The minor theorem [265] Exercises [268]
| Item type | Home library | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | 05 D564 (Browse shelf) | Available | A-7781 |
Traducción de: Graphentheorie. Springer-Verlag, 1996.
1. The Basics [1] --
1.1. Graphs [2] --
1.2. The degree of a vertex [4] --
1.3. Paths and cycles [6] --
1.4. Connectivity [9] --
1.5. Trees and forests [12] --
1.6. Bipartite graphs [13] --
1.7. Contraction and minors [15] --
1.8. Euler tours [17] --
1.9. Some linear algebra [19] --
1.10. Other notions of graphs [23] --
Exercises [25] --
Notes [26] --
2. Matching [29] --
2.1. Matching in bipartite graphs [29] --
2.2. Matching in general graphs [84] --
2.3. Path covers [38] --
Exercises --
Notes [42] --
3. Connectivity [43] --
3.1. 2-Connected graphs and subgraphs [43] --
3.2. The structure of 3-connected graphs [45] --
3.3. Menger’s theorem [50] --
3.4. Mader’s theorem [55] --
3.5. Edge-disjoint spanning trees [57] --
3.6. Paths between given pairs of vertices [60] --
Exercises [62] --
Notes [64] --
4. Planar Graphs [67] --
4.1. Topological prerequisites [68] --
4.2. Plane graphs [70] --
4.3. Drawings [77] --
4.4. Planar graphs: Kuratowski’s theorem [81] --
4.5. Algebraic planarity criteria [85] --
4.6. Plane duality [87] --
Exercises [90] --
Notes [92] --
5. Colouring [95] --
5.1. Colouring maps and planar graphs [96] --
5.2. Colouring vertices [98] --
5.3. Colouring edges [103] --
5.4. List colouring [105] --
5.5. Perfect graphs [110] --
Exercises [117] --
Notes [121] --
6. Flows [123] --
6.1. Circulations [124] --
6.2. Flows in networks [125] --
6.3. Group-valued flows [128] --
6.4. k-Flows for small k [133] --
6.5. Flow-colouring duality [136] --
6.6. Tutte’s flow conjectures [140] --
Exercises [144] --
Notes [146] --
7. Substructures in Dense Graphs [147] --
7.1. Subgraphs [148] --
7.2. Szemerédi’s regularity lemma [153] --
7.3. Applying the regularity lemma [160] --
Exercises [165] --
Notes [166] --
8. Substructures in Sparse Graphs [169] --
8.1. Topological minors [170] --
8.2. Minors [178] --
8.3. Hadwiger’s conjecture [180] --
Exercises [184] --
Notes [185] --
9. Ramsey Theory for Graphs [187] --
9.1. Ramsey’s original theorems [188] --
9.2. Ramsey numbers [191] --
9.3. Induced Ramsey theorems [194] --
9.4. Ramsey properties and connectivity [205] --
Exercises [206] --
Notes [208] --
10. Hamilton Cycles [211] --
10.1. Simple sufficient conditions [211] --
10.2. Hamilton cycles and degree sequences [214] --
10.3. Hamilton cycles in the square of a graph [216] --
Exercises [224] --
Notes [226] --
11. Random Graphs [227] --
11.1. The notion of a random graph [228] --
11.2. The probabilistic method [233] --
11.3. Properties of almost all graphs [236] --
11.4. Threshold functions and second moments [240] --
Exercises [245] --
Notes [247] --
12. Minors, Trees, and WQO [249] --
12.1. Well-quasi-ordering [249] --
12.2. The minor theorem for trees [251] --
12.3. Tree-decompositions [253] --
12.4. Tree-width and forbidden minors [257] --
12.5. The minor theorem [265] --
Exercises [268] --
MR, MR1448665
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