Colouring Diamond-free Graphs

The Colouring problem is that of deciding, given a graph G and an integer k, whether G admits a (proper) k-colouring. For all graphs H up to five vertices, we classify the computational complexity of Colouring for (diamond,H)-free graphs. Our proof is based on combining known results together with proving that the clique-width is bounded for (diamond,P_1+2P_2)-free graphs. Our technique for handling this case is to reduce the graph under consideration to a k-partite graph that has a very specific decomposition. As a by-product of this general technique we are also able to prove boundedness of clique-width for four other new classes of (H_1,H_2)-free graphs. As such, our work also continues a recent systematic study into the (un)boundedness of clique-width of (H_1,H_2)-free graphs, and our five new classes of bounded clique-width reduce the number of open cases from 13 to 8

Characteristics of Muskellunge Spermatozoa II: Effects of Ions and Osmolality on Sperm Motility

We investigated the effects of potassium, sodium, glucose, and calcium concentrations, alone or in combinations, on sperm motility in muskellunge Esox masquinongy. Sperm motility was evaluated by the duration of sperm movement and the initial percentage of motile sperm. The osmolality of diluents rather than the specific ions or nonelectrolyte played a major role in the regulation of sperm motility in muskellunge. Sperm were fully activated (>80%) when the concentration was lower than 50 mM of KCl and NaCl. or 100 mM glucose (all in 30 mM tris-HCl at pH 8.0). A small percent of spermatozoa could be activated at 150 mM KCl and NaCl. or 300 mM glucose, which were hypertonic to the seminal plasma. The duration of sperm movement was up to 6-7 min at 12°C in a solution of 100 mM glucose or 50 mM NaCl. Spermatozoa had a prolonged duration of movement in potassium solutions, up to 120 min at 12°C in a solution of 100 mM KC1. The prolonged duration of movement might be caused by reactivation of sperm or gradual activation of sperm molility. Calcium had an inhibitory effect on sperm motility in muskellunge, starting at 3 mM CaCl2 with 30 mM tris-HCl at pH 8.0. Semen diluted in calcium-supplemented solutions did not disperse well, and the sperm tended to form clumps. The mechanism involved in muskellunge sperm motility control markedly differs from that in salmonids (inhibitory function of K' and activatory role of Ca2') and cyprinids (no effect of Ca2' ).This work was funded by Piketon Research and Extension Center seed grant program and the Federal Aid in Sport Fish Restoration (project F-69-P, Fish Management in Ohio), administered jointly by the United States Fish and Wildlife Service and the Ohio Division of Wildlife. Salaries were partly provided by the state and federal funds appropriated to the Ohio Agriculture Research and Development Center (OARDC)

Structural solutions to maximum independent set and related problems

In this thesis, we study some fundamental problems in algorithmic graph theory. Most natural problems in this area are hard from a computational point of view. However, many applications demand that we do solve such problems, even if they are intractable. There are a number of methods in which we can try to do this: 1) We may use an approximation algorithm if we do not necessarily require the best possible solution to a problem. 2) Heuristics can be applied and work well enough to be useful for many applications. 3) We can construct randomised algorithms for which the probability of failure is very small. 4) We may parameterize the problem in some way which limits its complexity. In other cases, we may also have some information about the structure of the instances of the problem we are trying to solve. If we are lucky, we may and that we can exploit this extra structure to find efficient ways to solve our problem. The question which arises is - How far must we restrict the structure of our graph to be able to solve our problem efficiently? In this thesis we study a number of problems, such as Maximum Indepen- dent Set, Maximum Induced Matching, Stable-II, Efficient Edge Domina- tion, Vertex Colouring and Dynamic Edge-Choosability. We try to solve problems on various hereditary classes of graphs and analyse the complexity of the resulting problem, both from a classical and parameterized point of view