Geodesic
Laceable knights
Ars Mathematica Contemporanea, Tome 9 (2015) no. 1, pp. 115-124.

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A bipartite graph is Hamilton-laceable if for any two vertices in different parts there is a Hamiltonian path from one to the other. Using two main ideas (an algorithm for finding Hamiltonian paths and a decomposition lemma to move from smaller cases to larger) we show that the graph of knight’s moves on an m × n board is Hamilton-laceable iff m ≥ 6, n ≥ 6, and one of m, n is even. We show how the algorithm leads to new conjectures about Hamiltonian paths for various families, such as generalized Petersen graphs, I-graphs, and cubic symmetric graphs.
DOI : 10.26493/1855-3974.420.3c5
Keywords: Hamilton-laceable, generalized Petersen graphs, Hamilton-connected, Hamiltonian paths, knight graph, traceable 
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Michael Dupuis; Stan Wagon. Laceable knights. Ars Mathematica Contemporanea, Tome 9 (2015) no. 1, pp. 115-124. doi : 10.26493/1855-3974.420.3c5. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.420.3c5/

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