This thesis puts forward the conjecture that for <i>n</i> > 3<i>k</i> with <i>k</i> > 2, the generalized Petersen graph, <i>GP</i>(<i>n,k</i>) is Hamilton-laceable if <i>n</i> is even and <i>k</i> is odd, and it is Hamilton-connected otherwise. We take the first step in the proof of this conjecture by proving the case <i>n</i> = 3<i>k</i> + 1 and <i>k</i> greater than or equal to 1. We do this mainly by means of an induction which takes us from <i>GP</i>(3<i>k</i> + 1, <i>k</i>) to <i>GP</i>(3(<i>k</i> + 2) + 1, <i>k</i> + 2). The induction takes the form of mapping a Hamilton path in the smaller graph piecewise to the larger graph an inserting subpaths we call <i>rotors</i> to obtain a Hamilton path in the larger graph.

This thesis puts forward the conjecture that for <i>n</i> > 3<i>k</i> with <i>k</i> > 2, the generalized Petersen graph, <i>GP</i>(<i>n,k</i>) is Hamilton-laceable if <i>n</i> is even and <i>k</i> is odd, and it is Hamilton-connected otherwise. We take the first step in the proof of this conjecture by proving the case <i>n</i> = 3<i>k</i> + 1 and <i>k</i> greater than or equal to 1. We do this mainly by means of an induction which takes us from <i>GP</i>(3<i>k</i> + 1, <i>k</i>) to <i>GP</i>(3(<i>k</i> + 2) + 1, <i>k</i> + 2). The induction takes the form of mapping a Hamilton path in the smaller graph piecewise to the larger graph an inserting subpaths we call <i>rotors</i> to obtain a Hamilton path in the larger graph.

Many models in the physical and life sciences formulated as dynamical systems have a positive steady state, with the local behavior of this steady state determined by the eigenvalues of its Jacobian matrix. The first part of this thesis is concerned with analyzing the linear stability of the steady state by using sign patterns, which are matrices with entries from the set {+,-,0}. The linear stability is related to the allowed refined inertias of the sign pattern of the Jacobian matrix of the system, where the refined inertia of a matrix is a 4-tuple (n+, n_-, ; nz; 2np) with n+ (n_) equal to the number of eigenvalues with positive (negative) real part, nz equal to the number of zero eigenvalues, and 2np equal to the number of nonzero pure imaginary eigenvalues. This type of analysis is useful when the parameters of the model are of known sign but unknown magnitude. The usefulness of sign pattern analysis is illustrated with several biological examples, including biochemical reaction networks, predator{prey models, and an infectious disease model. The refined inertias allowed by sign patterns with specific digraph structures have been studied, for example, for tree sign patterns. In the second part of this thesis, such results on refined inertias are extended by considering sign and zero-nonzero patterns with digraphs isomorphic to strongly connected orientations of the Petersen graph. / Graduate

Philosophiae Doctor - PhD / The history of the pursuit of uncolourable cubic graphs dates back more than a century. This pursuit has evolved from the slow discovery of individual uncolourable cubic graphs such as the famous Petersen graph and the Blanusa snarks, to discovering in nite classes of uncolourable cubic graphs such as the Louphekine and Goldberg snarks, to investigating parameters which measure the uncolourability of cubic graphs. These parameters include resistance, oddness and weak oddness, ow resistance, among others. In this thesis, we consider current ideas and problems regarding the uncolourability of cubic graphs, centering around these parameters. We introduce new ideas regarding the structural complexity of these graphs in question. In particular, we consider their 3-critical subgraphs, speci cally in relation to resistance. We further introduce new parameters which measure the uncolourability of cubic graphs, speci cally relating to their 3-critical subgraphs and various types of cubic graph reductions. This is also done with a view to identifying further problems of interest. This thesis also presents solutions and partial solutions to long-standing open conjectures relating in particular to oddness, weak oddness and resistance.

Zugl.: Frankfurt (Main), Univ., Habil.-Schr., 2008

The black caiman (Melanosuchus niger) and the yacare caiman (Caiman yacare) have in the past been exposed to overexploitation due to the economic profit for their hides, and therefore suffered from great declines in population sizes, especially black caimans. Legal regulation efforts made it possible for these two species to recover and today they are widely distributed in South America. Evaluation of protection and management of populations of top predators like these caimans depend on the ability to detect the animals. The probability of detecting a crocodile, or any animal, is affected by several factors such as habitat complexity and behaviour why it is of importance to acknowledge such matter in order to obtain reliable results for further implications. This study aims to investigate the detection probability and abundances in these two species as a contribution to the monitoring efforts at a local scale. Night counts were performed in Cedral lagoon located in the Beni region in Bolivia. By using the relation between marked animals and resightings of them, as well as the abundance estimate produced by the Lincoln-Petersen estimator, estimates of detection probabilities could be accounted for the total caiman population (black plus yacare caimans) and the black caiman population. Very low sighting probabilities (p = 0.03) were obtained when based on marked animals who tend to be more wary after a capture event. Those based on the L-P output were higher (total caiman population p = 0.15, black caimans p = 0.15). Population sizes were estimated to 25 ± 8.5 black caimans and 34 ± 12 caimans in total. The population size based on marked animals was 12 ± 25.4 caimans.

Abstracts THE TAINT This is a memoir of Ray “Poss” Ide, a man who has carried the taint of a horrifying crime since he was seventeen years old─a crime he claims he did not commit. The crime was the rape of a fourteen-year-old girl. The Taint looks at the time leading up to his conviction for rape, including the years he spent in Westbrook Boys’ Reformatory and Boggo Road Gaol as a minor, and then his sentence served in NSW gaols with such inmates as Stephen Bradley, the man who kidnapped and murdered Graham Thorne, and the bizarre but rather likeable Dave Scanlan, known for his exploits as “the Kingsgrove Slasher”. In prison, Scanlan encouraged him to become an elite sportsman and released, Poss was recruited by Canterbury Eels football team; but just on the point of making a name for himself in Sydney, someone discovered that he had been gaoled for rape, and humiliated, he left the team. He moved back home to Queensland via Grafton, NSW (where he met and later married the Jacaranda Queen) and continued his sporting career, but never again in the Big League. He became the Manager of the Waterside Workers’ Club and helped prevent a turf war between the Wharfies and members of the Painters and Dockers. Poss is now working with lawyer Robert Bax to have his case re-opened. He believes his story to be a cautionary tale for young men. It is a chronicle of social change, including the sexual revolution of the sixties, the confrontations with “the demons” in the streets of Brisbane during the Joh era of Bible-bashing fundamentalism and police corruption. It’s a story about what really went on behind closed doors in institutions where vulnerable children were preyed upon, in gaols where men were expected to become beasts. It is a story of how the taint of a terrible crime affected a man’s whole life. “QUESTIONS OF OWNERSHIP” Writing someone else’s story can be an ethical minefield─especially regarding questions of ownership. Who owns the story, the subject or the author? The easy answer to this is the subject owns the story and the author the text, but on closer examination this may not necessarily be so. Then there are those other stakeholders who claim ownership of story: people who embrace a narrative because of its similarity to their own lives. Published stories about institutional abuse have resonated for adults who as children were placed into the care of churches or the state. Another kind of ownership is claimed by readers who accept a version of a story and dismiss any counter-story as being invalid. What I call the “Plath Phenomenon” is an example of this. I will examine these kinds of ownership of story with particular reference to the work of Janet Malcolm on biography and then will look at gaps and silences in “official” stories, those created in police stations and courtrooms.

Abstracts THE TAINT This is a memoir of Ray “Poss” Ide, a man who has carried the taint of a horrifying crime since he was seventeen years old─a crime he claims he did not commit. The crime was the rape of a fourteen-year-old girl. The Taint looks at the time leading up to his conviction for rape, including the years he spent in Westbrook Boys’ Reformatory and Boggo Road Gaol as a minor, and then his sentence served in NSW gaols with such inmates as Stephen Bradley, the man who kidnapped and murdered Graham Thorne, and the bizarre but rather likeable Dave Scanlan, known for his exploits as “the Kingsgrove Slasher”. In prison, Scanlan encouraged him to become an elite sportsman and released, Poss was recruited by Canterbury Eels football team; but just on the point of making a name for himself in Sydney, someone discovered that he had been gaoled for rape, and humiliated, he left the team. He moved back home to Queensland via Grafton, NSW (where he met and later married the Jacaranda Queen) and continued his sporting career, but never again in the Big League. He became the Manager of the Waterside Workers’ Club and helped prevent a turf war between the Wharfies and members of the Painters and Dockers. Poss is now working with lawyer Robert Bax to have his case re-opened. He believes his story to be a cautionary tale for young men. It is a chronicle of social change, including the sexual revolution of the sixties, the confrontations with “the demons” in the streets of Brisbane during the Joh era of Bible-bashing fundamentalism and police corruption. It’s a story about what really went on behind closed doors in institutions where vulnerable children were preyed upon, in gaols where men were expected to become beasts. It is a story of how the taint of a terrible crime affected a man’s whole life. “QUESTIONS OF OWNERSHIP” Writing someone else’s story can be an ethical minefield─especially regarding questions of ownership. Who owns the story, the subject or the author? The easy answer to this is the subject owns the story and the author the text, but on closer examination this may not necessarily be so. Then there are those other stakeholders who claim ownership of story: people who embrace a narrative because of its similarity to their own lives. Published stories about institutional abuse have resonated for adults who as children were placed into the care of churches or the state. Another kind of ownership is claimed by readers who accept a version of a story and dismiss any counter-story as being invalid. What I call the “Plath Phenomenon” is an example of this. I will examine these kinds of ownership of story with particular reference to the work of Janet Malcolm on biography and then will look at gaps and silences in “official” stories, those created in police stations and courtrooms.

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