Geodesic
Types of triangle in Hamiltonian triangulations and an application to domination and k-walks
Ars Mathematica Contemporanea, Tome 17 (2019) no. 1, pp. 51-66.

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We investigate the minimum number t0(G) of faces in a Hamiltonian triangulation G so that any Hamiltonian cycle C of G has at least t0(G) faces that do not contain an edge of C. We prove upper and lower bounds on the maximum of these numbers for all triangulations with a fixed number of facial triangles. Such triangles play an important role when Hamiltonian cycles in triangulations with 3-cuts are constructed from smaller Hamiltonian cycles of 4-connected subgraphs. We also present results linking the number of these triangles to the length of 3-walks in a class of triangulation and to the domination number.
DOI : 10.26493/1855-3974.1733.8c6
Keywords: Graph, Hamiltonian cycle, domination, 3-walk 
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Gunnar Brinkmann; Kenta Ozeki; Nico Van Cleemput. Types of triangle in Hamiltonian triangulations and an application to domination and k-walks. Ars Mathematica Contemporanea, Tome 17 (2019) no. 1, pp. 51-66. doi : 10.26493/1855-3974.1733.8c6. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.1733.8c6/

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