Every 3-polytope with minimum degree 5 has a 6-cycle with maximum degree at most 11
2013; Elsevier BV; Volume: 315-316; Linguagem: Inglês
10.1016/j.disc.2013.10.021
ISSN1872-681X
AutoresO. V. Borodin, A. O. Ivanova, Alexandr Kostochka,
Tópico(s)Computational Geometry and Mesh Generation
ResumoLet φP(C6) (respectively, φT(C6)) be the minimum integer k with the property that every 3-polytope (respectively, every plane triangulation) with minimum degree 5 has a 6-cycle with all vertices of degree at most k. In 1999, S. Jendrol' and T. Madaras proved that 10≤φT(C6)≤11. It is also known, due to B. Mohar, R. Škrekovski and H.-J. Voss (2003), that φP(C6)≤107. We prove that φP(C6)=φT(C6)=11.
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