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Circuit visiting 10 ordered vertices in infinite grids
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+1}} \in 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.
Cited literature [21 references]
https://hal.inria.fr/inria-00378586
Contributor : David Coudert <>
Submitted on : Friday, April 24, 2009 - 5:25:57 PM
Last modification on : Tuesday, June 22, 2021 - 8:14:03 PM
Long-term archiving on: : Friday, October 12, 2012 - 5:16:07 PM
Contributor : David Coudert <>
Submitted on : Friday, April 24, 2009 - 5:25:57 PM
Last modification on : Tuesday, June 22, 2021 - 8:14:03 PM
Long-term archiving on: : Friday, October 12, 2012 - 5:16:07 PM
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RR-6910.pdf
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