A5076508424- graph theory and CDMA systems
- Coding theory and cryptography
- Finite Group Theory Research
- Limits and Structures in Graph Theory
- Graph Labeling and Dimension Problems
- Optimal Experimental Design Methods
- Advanced Graph Theory Research
- Graph theory and applications
- Mathematical Approximation and Integration
- VLSI and FPGA Design Techniques
- Advanced Wireless Communication Techniques
- Cellular Automata and Applications
- semigroups and automata theory
- Optimization and Packing Problems
- Mobile Ad Hoc Networks
- Cooperative Communication and Network Coding
- Energy Efficient Wireless Sensor Networks
- Cold Atom Physics and Bose-Einstein Condensates
- Advanced Topology and Set Theory
- Manufacturing Process and Optimization
- Markov Chains and Monte Carlo Methods
- Chronic Lymphocytic Leukemia Research
- Analytic Number Theory Research
- Machine Learning and Algorithms
- Point processes and geometric inequalities
University of Victoria
2014-2023
University of Perugia
2021-2022
Natural Sciences and Engineering Research Council
2014
Statistics Canada
2014
Medical Research Council
2009
Universidad de Londres
2006
Victoria University
2006
University of Toronto
1999-2004
California Institute of Technology
2002-2003
Data sharing, and the good annotation practices it depends on, must become part of fabric daily research for researchers funders.
In this paper, we consider a weakening of the definitions uniform and perfect one-factorizations complete graph. Basically, want to order $2n-1$ one-factors one-factorization graph $K_{2n}$ in such way that union any two (cyclically) consecutive is always isomorphic same two-regular This property termed sequentially uniform; if Hamiltonian cycle, then perfect. We will discuss several methods for constructing one-factorizations. particular, prove integer $n \geq 1$ there $K_{2n}$. As well,...
Abstract Let v ≥ k 1 and λ 0 be integers. A block design BD( , λ) is a collection of -subsets -set X in which every unordered pair elements from contained exactly . More generally, for fixed simple graph G GD( graphs isomorphic to with vertices such that an edge famous result Wilson says λ, there exists all sufficiently large satisfying certain necessary conditions. (graph) as above resolvable if can partitioned into partitions (graphs whose vertex sets partition) Lu has shown asymptotic...
Abstract A group divisible design (GDD) is a triple which satisfies the following properties: (1) partition of X into subsets called groups; (2) collection , blocks, such that and block contain at most one element in common; (3) every pair elements from distinct groups occurs constant number λ blocks. This parameter usually index. k ‐GDD type GDD with size index u g . resolvable if blocks can be partitioned classes each point precisely class. We denote as an RGDD. For fixed integers we show...
Abstract An incomplete pairwise balanced design is equivalent to a with distinguished block, viewed as ‘hole’. If there are v points, hole of size w, and all (other) block sizes equal k, this denoted IPBD((v;w), k). In addition congruence restrictions on also necessary inequality: > (k − 1)w. This article establishes two main existence results for k): one in which w fixed large, the other case −1+∊)w when large (depending ∊). Several possible generalizations problemare discussed.
We compute a minimum degree threshold sufficient for 3-partite graphs to admit fractional triangle decomposition. Together with recent work of Barber, K\uhn, Lo, Osthus and Taylor, this leads bounds exact decompositions in particular the completion problem sparse partial latin squares. Some extensions are considered as well.
Medium access control for multihop wireless sensor networks (WSNs) must be energy efficient because the battery-operated nodes are not practical to recharge. We give constructions ternary schedules in which each node is one of three states: transmitting, receiving, or asleep. For hop (v <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">i</sub> , v xmlns:xlink="http://www.w3.org/1999/xlink">j</sub> ), communication effective only when and no other...
We consider the problem of decomposing some $t$-uniform hypergraph $G$ into copies another, say $H$, with nonnegative rational weights. For fixed $H$ on $k$ vertices, we show that this is always possible for all having sufficiently many vertices and `local density' at least $1-C(t)k^{-2t}$. In case $t=2$ $H=K_3$, large graphs density $27/28$ admit a fractional triangle decomposition. The proof relies estimates certain eigenvalues in Johnson scheme.