Graph universal cycles: Compression and connections to universal cycles

Universal cycles, such as De Bruijn are cyclic sequences of symbols that represent every combinatorial object from some family exactly once a consecutive subsequence. Graph universal cycles graph analogue introduced in 2010. We introduce partial more compact representation classes, which use “do not know” edges. show how to construct for labeled graphs, threshold and permutation graphs. For graphs we demonstrate the closely related compressed respectively. Using same connection, define prove existence an s-overlap form cycles. also generalized unlabeled