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Full-Text Articles in Physical Sciences and Mathematics

Nested Balanced Incomplete Block Designs, J. P. Morgan, D. A. Preece, D. H. Rees Jan 2001

Nested Balanced Incomplete Block Designs, J. P. Morgan, D. A. Preece, D. H. Rees

Mathematics & Statistics Faculty Publications

If the blocks of a balanced incomplete block design (BIBD) with v treatments and with parameters (v; b1;r;k1) are each partitioned into sub-blocks of size k2, and the b2 =b1k1=k2 sub-blocks themselves constitute a BIBD with parameters (v; b2;r;k2), then the system of blocks, sub-blocks and treatments is, by de4nition, a nested BIBD (NBIBD). Whist tournaments are special types of NBIBD with k1 =2k2= 4. Although NBIBDs were introduced in the statistical literature in 1967 and have subsequently received occasional attention there, …


Efficient Algorithms For Graphs With Few P-4’S, Luitpold Babel, Ton Kloks, Jan Kratochvíl, Dieter Kratsch, Kaiko Müller, Stephan Olariu Jan 2001

Efficient Algorithms For Graphs With Few P-4’S, Luitpold Babel, Ton Kloks, Jan Kratochvíl, Dieter Kratsch, Kaiko Müller, Stephan Olariu

Computer Science Faculty Publications

We show that a large variety of NP-complete problems can be solved efficiently for graphs with 'few' P4's. We consider domination problems (domination, total domination, independent domination. connected domination and dominating clique), the Steiner tree problem, the vertex ranking problem, the pathwidth problem, the path cover number problem, the hamiltonian circuit problem, the list coloring problem and the precoloring extension problem. We show that all these problems can be solved in linear time for the class of (q,q - 4)-graphs, for every fixed q. These are graphs for which no set of at most q. vertices induces more …