CanaDAM 2011
University of Victoria, May 31 - June 3, 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.

Handling of online submissions has been provided by the CMS.

Event Sponsors

Centre de recherches mathématiques Fields Institute MITACS Pacific Institute for the Mathematical Sciences Canadian Mathematical Society University of Victoria