Combinatorial questions: how can graph labelling help?

We highlight some connections between graph labelling, combinatorial design theory and information theory. We survey results on the construction and enumeration of Skolem labellings and related structures. This includes discussion of two constructions of low density parity check codes from Skolem labellings. We raise several pertinent questions and suggestions for future research directions

Uniformly Resolvable Cycle Decompositions with Four Different Factors

In this paper, we consider uniformly resolvable decompositions of complete graph K-v( or K-v minus a 1-factor I for even v) into cycles. We will focus on the existence of factorizations of K-v or K-v - I containing up to four non-isomorphic factors. We obtain all possible solutions for uniform factors involving 4, m, 2m and 4m-cycles with a few possible exceptions when m is odd