CanaDAM 2011
Université de Victoria, 31 mai - 3 juin 2011

Combinatorial Designs, Codes and Graph Factors

ATIF ABUEIDA, University of Dayton
The spectrum of non-polychromatic equitable edge colored Steiner Triple Systems  [PDF]

A $STS(v)$ is called polychromatic if the edges of every triple in the $STS(v)$ is colored with three different colors. We discuss the relation between equitable $k$-edge coloring of $K_{v}$ and polychromatic $STS(v)$ when $2 \leq k \leq v-2$. This is joint work with James Lefevre and Mary Waterhouse.

MELISSA KERANEN, Michigan Technological University
GDDs with two groups and block size 6 with fixed block configuration  [PDF]

A $GDD(n,2, k; \lambda_1, \lambda_2)$ has fixed block configuration $(s, t)$ if each block has exactly $s$ points from one group and $k-s = t$ points from the other. We give new results on the existence of $GDD(n,2,6; \lambda_1, \lambda_2)$s with fixed block configurations $(3,3)$, $(4,2)$ and $(5,1)$. (Joint work with Melanie Laffin.)

NIDHI SEHGAL, Auburn University
$6$-cycle system of the cartesian product $K_x \times K_y$ covering $2$-paths in $K_{x,y}$  [PDF]

A cycle in $G_1 \times G_2$ is said to be \textsl{fair} if it has atmost two vertices in each row and in each column. Notions of \textsl{fairness} in graph decompositions have arisen in various forms, such as \textsl{equitable} and \textsl{gregarious} decompositions. In this talk, we give necessary and sufficient conditions, and the required constructions to obtain a \textsl{fair} $(C_6, P_2)$ $1$-covering of $K_s \times K_t$ which yields a $(C_6, P_3)$ $1$-covering of $K(S,T)$.

PADMAPANI SENEVIRATNE, American University of Sharjah
Codes from multipartite graphs and permutation decoding  [PDF]

We examine the self orthogonal codes associated with the row-span of incidence matrices and the adjacency matrices of complete multi-partite graphs and we show that, these codes contain permutation decoding sets or PD-sets for full-error correction. Further we study the computational complexity of the permutation decoding method.

CHINA VENKAIAH VADLAMUDI, C R Rao Advanced Institute of Mathematics, Statistics, and Computer Science
Sequentially Perfect 1-Factorization and Cycle Structure of Patterned Factorization of $K_{2^{n}}$  [PDF]

In this paper, a new method to construct a 1-factorization of a complete graph of order $2^{n}$ is proposed. Novelty of the method is that the 1-factorization that it produces is sequentially perfect and is at times perfect. Also, a set of 1-factors of the 1-factorization are always pairwise perfect. These perfect pairs can be identified using the gcd computation. The paper also analyzes the cycle structure of the patterned 1-factorization via the proposed 1-factorization.

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Centre de recherches mathématiques Fields Institute MITACS Pacific Institute for the Mathematical Sciences Société mathématique du Canada University of Victoria