Multi de Bruijn sequences

Tesler, Glenn

doi:10.4310/joc.2017.v8.n3.a3

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F -Fold Gucycles For Unlabeled Graphs1

Introduction1

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Cited by 2 publications

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“…In analogy to f -fold De Bruijn cycles, introduced by Tesler [23], we define f -fold gucycles as follows.…”

Section: F -Fold Gucycles For Unlabeled Graphsmentioning

confidence: 99%

Graph Universal Cycles: Compression and Connections to Universal Cycles

Kirsch¹,

Sibley²,

Sprangel³

2022

Preprint

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

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“…In analogy to f -fold De Bruijn cycles, introduced by Tesler [23], we define f -fold gucycles as follows.…”

Section: F -Fold Gucycles For Unlabeled Graphsmentioning

confidence: 99%

Graph Universal Cycles: Compression and Connections to Universal Cycles

Kirsch¹,

Sibley²,

Sprangel³

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…A corresponding de Bruijn sequence is 220011210. For further results on de Bruijn sequences and graphs on larger alphabets, see [1,3,7,11]. Given a graph G and a single watchman, the watchman's walk problem looks at the scenario of that watchman traversing the graph in such a way that the route is a minimum closed dominating walk.…”

Section: Introductionmentioning

confidence: 99%