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- W2144802729 abstract "A circuit in a simple undirected graph G = (V,E) is a sequence of vertices {v 1,v 2,...,v k + 1} such that v 1 = v k + 1 and {v i ,v i + i } ∈ E for i = 1,...,k. A circuit C is said to be edge-simple if no edge of G is used twice in C. In this article we study the following problem: which is the largest integer k such that, given any subset of k ordered vertices of an infinite square grid, there exists an edge-simple circuit visiting the k vertices in the prescribed order? We prove that k = 10. To this end, we first provide a counterexample implying that k < 11. To show that k ≥ 10, we introduce a methodology, based on the notion of core graph, to reduce drastically the number of possible vertex configurations, and then we test each one of the resulting configurations with an ILP solver." @default.
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- W2144802729 date "2009-01-01" @default.
- W2144802729 modified "2023-09-24" @default.
- W2144802729 title "Edge-Simple Circuits through 10 Ordered Vertices in Square Grids" @default.
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- W2144802729 doi "https://doi.org/10.1007/978-3-642-10217-2_16" @default.
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