Abstract
We present a family of graphs implicitly involved in sequential models, which are obtained by adding edges between elements of a discrete sequence appearing simultaneously in a window of size w, and study their combinatorial properties. First, we study the conditions for a graph to be a sequence graph. Second, we provide, when possible, the number of sequences it represents. For w = 2, unweighted 2-sequence graphs are simply connected graphs, whereas unweighted 2-sequence digraphs form a less trivial family. The decision and counting for weighted 2-sequence graphs can be transformed by reduction into Eulerian graph problems. Finally, we present a polynomial time algorithm to decide if an undirected and unweighted graph has the said property for w ≥ 3. The question of NP-hardness is left opened for other cases.
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Khalife, S. (2021). Sequence Graphs: Characterization and Counting of Admissible Elements. In: Gentile, C., Stecca, G., Ventura, P. (eds) Graphs and Combinatorial Optimization: from Theory to Applications. AIRO Springer Series, vol 5. Springer, Cham. https://doi.org/10.1007/978-3-030-63072-0_17
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DOI: https://doi.org/10.1007/978-3-030-63072-0_17
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