Displaying similar documents to “On the monotone upper bound problem.”

All Tight Descriptions of 3-Stars in 3-Polytopes with Girth 5

Oleg V. Borodin, Anna O. Ivanova (2017)

Discussiones Mathematicae Graph Theory


Lebesgue (1940) proved that every 3-polytope P5 of girth 5 has a path of three vertices of degree 3. Madaras (2004) refined this by showing that every P5 has a 3-vertex with two 3-neighbors and the third neighbor of degree at most 4. This description of 3-stars in P5s is tight in the sense that no its parameter can be strengthened due to the dodecahedron combined with the existence of a P5 in which every 3-vertex has a 4-neighbor. We give another tight description of 3-stars in P5s:...

Sections of simplices.

Prabhu, Nagabhushana (1999)

International Journal of Mathematics and Mathematical Sciences


On the refinements of a polyhedral subdivision.

Francisco Santos (2001)

Collectanea Mathematica


Let pi: P --> Q be an affine projection map between two polytopes P and Q. Billera and Sturmfels introduced in 1992 the concept of polyhedral subdivisions of Q induced by pi (or pi-induced) and the fiber polytope of the projection: a polytope Sygma(P,pi) of dimension dim(P)-dim(Q) whose faces are in correspondence with the coherent pi-induced subdivisions (or pi-coherent subdivisions). In this paper we investigate the structure of the poset of pi-induced refinements of a pi-induced...