Some aspects of the theory of circulant graphs

**Authors:**Hattingh, Johannes Hendrik**Date:**2014-03-18**Subjects:**Graphic methods , Conformal geometry**Type:**Thesis**Identifier:**uj:4390 , http://hdl.handle.net/10210/9738**Description:**Ph.D. (Mathematics) , Please refer to full text to view abstract**Full Text:**

**Authors:**Hattingh, Johannes Hendrik**Date:**2014-03-18**Subjects:**Graphic methods , Conformal geometry**Type:**Thesis**Identifier:**uj:4390 , http://hdl.handle.net/10210/9738**Description:**Ph.D. (Mathematics) , Please refer to full text to view abstract**Full Text:**

Generalized chromatic numbers and invariants of hereditary graph properties

**Authors:**Dorfling, Samantha**Date:**2011-12-06**Subjects:**Invariants , Graphic methods , Graph theory**Type:**Thesis**Identifier:**uj:1784 , http://hdl.handle.net/10210/4149**Description:**D. Phil (Mathematics) , In this thesis we investigate generalized chromatic numbers in the context of hereditary graph properties. We also investigate the general topic of invariants of graphs as well as graph properties. In Chapter 1 we give relevant definitions and terminology pertaining to graph properties. In Chapter 2 we investigate generalized chromatic numbers of some well-known additive hereditary graph properties. This problem necessitates the investigation of reducible bounds. One of the results here is an improvement on a known upper bound for the path partition number of the property Wk. We also look at the generalized chromatic number of infinite graphs and hereby establish the connection between the generalized chromatic number of properties and infinite graphs. In Chapter 3 the analogous question of the generalized edge-chromatic number of some well-known additive hereditary properties is investigated. Similarly we find decomposable bounds and are also able to find generalized edge-chromatic numbers of properties using some well-known decomposable bounds. In Chapter 4 we investigate the more general topic of graph invariants and the role they play in chains of graph properties and then conversely the invariants that arise from chains of graph properties. Moreover we investigate the effects on monotonicity of the invariants versus heredity and additivity of graph properties. In Chapter 5 the general topic of invariants of graph properties defined in terms of the set of minimal forbidden subgraphs of the properties is studied. This enables us to investigate invariants so defined on binary operations between graph properties. In Chapter 6 the notion of natural and near-natural invariants are introduced and are also studied on binary operations of graph properties. The set of minimal forbidden subgraphs again plays a role in the definition of invariants here and this then leads us to study the completion number of a property.**Full Text:**

**Authors:**Dorfling, Samantha**Date:**2011-12-06**Subjects:**Invariants , Graphic methods , Graph theory**Type:**Thesis**Identifier:**uj:1784 , http://hdl.handle.net/10210/4149**Description:**D. Phil (Mathematics) , In this thesis we investigate generalized chromatic numbers in the context of hereditary graph properties. We also investigate the general topic of invariants of graphs as well as graph properties. In Chapter 1 we give relevant definitions and terminology pertaining to graph properties. In Chapter 2 we investigate generalized chromatic numbers of some well-known additive hereditary graph properties. This problem necessitates the investigation of reducible bounds. One of the results here is an improvement on a known upper bound for the path partition number of the property Wk. We also look at the generalized chromatic number of infinite graphs and hereby establish the connection between the generalized chromatic number of properties and infinite graphs. In Chapter 3 the analogous question of the generalized edge-chromatic number of some well-known additive hereditary properties is investigated. Similarly we find decomposable bounds and are also able to find generalized edge-chromatic numbers of properties using some well-known decomposable bounds. In Chapter 4 we investigate the more general topic of graph invariants and the role they play in chains of graph properties and then conversely the invariants that arise from chains of graph properties. Moreover we investigate the effects on monotonicity of the invariants versus heredity and additivity of graph properties. In Chapter 5 the general topic of invariants of graph properties defined in terms of the set of minimal forbidden subgraphs of the properties is studied. This enables us to investigate invariants so defined on binary operations between graph properties. In Chapter 6 the notion of natural and near-natural invariants are introduced and are also studied on binary operations of graph properties. The set of minimal forbidden subgraphs again plays a role in the definition of invariants here and this then leads us to study the completion number of a property.**Full Text:**

Karakterisering van planêre grafieke

**Authors:**Wilson, Bònita Sintiché**Date:**1995**Subjects:**Graph theory**Language:**Afrikaans**Type:**Masters Thesis**Identifier:**http://hdl.handle.net/10210/21548 , uj:16147**Description:**Abstract: A graph is called planar if it can be represented on the plane without points of intersection of lines. It is clear from the title that this study is concerned with the characterization of such graphs. In Paragraph 1.2 notation and terminology that are needed throughout, are defined. Specialized notation and terminology are defined when needed. Chapter 2 is concerned with the characterization of planar graphs in terms of forbidden subgraphs. In this regard, specific attention is given to a proof of the Theorem of Kuratowski. In Chapter 3 we prove the characterizations of planar graphs in terms of partially ordered sets of Schnyder and Scheinerman. In Chapter 4 a few characterizations of planar graphs (without proof) are presented. These results of planar graphs are used collectively to state a characterization in Paragraph 4.3. , M.A. (Mathematics)**Full Text:**

**Authors:**Wilson, Bònita Sintiché**Date:**1995**Subjects:**Graph theory**Language:**Afrikaans**Type:**Masters Thesis**Identifier:**http://hdl.handle.net/10210/21548 , uj:16147**Description:**Abstract: A graph is called planar if it can be represented on the plane without points of intersection of lines. It is clear from the title that this study is concerned with the characterization of such graphs. In Paragraph 1.2 notation and terminology that are needed throughout, are defined. Specialized notation and terminology are defined when needed. Chapter 2 is concerned with the characterization of planar graphs in terms of forbidden subgraphs. In this regard, specific attention is given to a proof of the Theorem of Kuratowski. In Chapter 3 we prove the characterizations of planar graphs in terms of partially ordered sets of Schnyder and Scheinerman. In Chapter 4 a few characterizations of planar graphs (without proof) are presented. These results of planar graphs are used collectively to state a characterization in Paragraph 4.3. , M.A. (Mathematics)**Full Text:**

Generalised colourings of graphs

**Authors:**Frick, Marietjie**Date:**2015-10-07**Subjects:**Representations of graphs , Graph theory**Type:**Thesis**Identifier:**uj:14233 , http://hdl.handle.net/10210/14686**Description:**Ph.D. , Please refer to full text to view abstract**Full Text:**

**Authors:**Frick, Marietjie**Date:**2015-10-07**Subjects:**Representations of graphs , Graph theory**Type:**Thesis**Identifier:**uj:14233 , http://hdl.handle.net/10210/14686**Description:**Ph.D. , Please refer to full text to view abstract**Full Text:**

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