Hedetniemi’s Conjecture and Adjoint Functors in Thin Categories

We survey results on Hedetniemi’s conjecture which are connected to adjoint functors in the “thin” category of graphs, and expose the obstacles to extending these results

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