### Flag vectors of multiplicial polytopes.

Bayer, Margaret M. (2004)

The Electronic Journal of Combinatorics [electronic only]

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Bayer, Margaret M. (2004)

The Electronic Journal of Combinatorics [electronic only]

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S. Jendrol, E. Jucovič, M. Trenkler (1989)

Banach Center Publications

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Fusy, Éric (2006)

The Electronic Journal of Combinatorics [electronic only]

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Lee, Carl W. (2011)

The Electronic Journal of Combinatorics [electronic only]

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Athanasiadis, Christos A. (2004)

The Electronic Journal of Combinatorics [electronic only]

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Branko Grünbaum, Ernest Jucovič (1974)

Czechoslovak Mathematical Journal

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R. Blind, G. Blind (1994)

Discrete & computational geometry

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Schwartz, Alexander, Ziegler, Günter M. (2004)

Experimental Mathematics

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

Discussiones Mathematicae Graph Theory

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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:...

R. Blind, G. Blind (1995)

Discrete & computational geometry

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Prabhu, Nagabhushana (1999)

International Journal of Mathematics and Mathematical Sciences

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Francisco Santos (2001)

Collectanea Mathematica

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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...