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A closed convex subset C of a Banach space X is called approximatively polyhedral if for each ε > 0 there is a polyhedral (= intersection of finitely many closed half-spaces) convex set P ⊂ X at Hausdorff distance < ε from C. We characterize approximatively polyhedral convex sets in Banach spaces and apply the characterization to show that a connected component of the space $C o n v_{} (X)$ of closed convex subsets of X endowed with the Hausdorff metric is separable if and only if contains a polyhedral convex...

A New Necessary Condition for the Vertex Visibility Graphs of Simple Polygons.

G. Srinivasaraghavan, A. Mukhopadhyay (1994)

Discrete & computational geometry

A point in many triangles.

Bukh, Boris (2006)

The Electronic Journal of Combinatorics [electronic only]

A simpler construction of volume polynomials for a polyhedron.

Lawrencenko, Serge, Negami, Seiya, Sabitov, Idjad Kh. (2002)

Beiträge zur Algebra und Geometrie

A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria

Pedro A. Góngora, David A. Rosenblueth (2015)

International Journal of Applied Mathematics and Computer Science

Consider games where players wish to minimize the cost to reach some state. A subgame-perfect Nash equilibrium can be regarded as a collection of optimal paths on such games. Similarly, the well-known state-labeling algorithm used in model checking can be viewed as computing optimal paths on a Kripke structure, where each path has a minimum number of transitions. We exploit these similarities in a common generalization of extensive games and Kripke structures that we name “graph games”. By extending...

Algebraic shifting and sequentially Cohen-Macaulay simplicial complexes.

Duval, Art M. (1996)

The Electronic Journal of Combinatorics [electronic only]

Algorithms for Triangulating Polyhedra Into a Small Number of Tethraedra

Milica Stojanović (2005)

Matematički Vesnik

An inequality concerning edges of minor weight in convex 3-polytopes

Igor Fabrici, Stanislav Jendrol' (1996)

Discussiones Mathematicae Graph Theory

Let $e_{i j}$ be the number of edges in a convex 3-polytope joining the vertices of degree i with the vertices of degree j. We prove that for every convex 3-polytope there is $20 e_{3, 3} + 25 e_{3, 4} + 16 e_{3, 5} + 10 e_{3, 6} + 6 [2 / 3] e_{3, 7} + 5 e_{3, 8} + 2 [1 / 2] e_{3, 9} + 2 e_{3, 10} + 16 [2 / 3] e_{4, 4} + 11 e_{4, 5} + 5 e_{4, 6} + 1 [2 / 3] e_{4, 7} + 5 [1 / 3] e_{5, 5} + 2 e_{5, 6} \geq 120$ ; moreover, each coefficient is the best possible. This result brings a final answer to the conjecture raised by B. Grünbaum in 1973.

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1-bend 3-D orthogonal box-drawings: Two open problems solved.

A Bound on Local Minima of Arrangements that Implies the Upper Bound Theorem.

A Characterisation of a Simplex.

A combinatorial proof of a formula for Betti numbers of a stacked polytope.

A construction for periodically-cyclic Gale $2 m$ -polytopes.

A Decomposition of 2-Weak Vertex-Packing Polytopes.

A Generalization of Dehn-Sommerville Relations to Simple Stratified Spaces.

A "hidden" characterization of approximatively polyhedral convex sets in Banach spaces

A New Necessary Condition for the Vertex Visibility Graphs of Simple Polygons.

A point in many triangles.

A simpler construction of volume polynomials for a polyhedron.

A symbolic shortest path algorithm for computing subgame-perfect Nash equilibria

Algebraic shifting and sequentially Cohen-Macaulay simplicial complexes.

Algorithms for Triangulating Polyhedra Into a Small Number of Tethraedra

An inequality concerning edges of minor weight in convex 3-polytopes

Automorphismen von polyedrischen Graphen.

Bemerkungen zu Determinanten-Theorie. Auszug aus Briefen an Herrn Baltzer.

Bergman complexes, Coxeter arrangements, and graph associahedra.

Bose's vertex theorem for simply closed polygons.

Cardinality estimates for piecewise congruences of convex polygons.

Currently displaying 1 – 20 of 108