Elsevier

Discrete Mathematics

Volumes 315–316, 6 February 2014, Pages 128-134
Discrete Mathematics

Every 3-polytope with minimum degree 5 has a 6-cycle with maximum degree at most 11

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Abstract

Let 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 10φT(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.

Keywords

Planar graph
Plane map
Structure properties
3-polytope
Weight

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