Tag Archives: Micha A. Perles

Open problem session of HUJI-COMBSEM: Problem #2 Chaya Keller: The Krasnoselskii number

  Marilyn Breen This is our second post on the open problem session of the HUJI combinatorics seminar. The video of the session is here. Today’s problem was presented by Chaya Keller. The Krasnoselskii number One of the best-known applications … Continue reading

Posted in Combinatorics, Convexity | Tagged , , , | 4 Comments

Micha Perles’ Geometric Proof of the Erdos-Sos Conjecture for Caterpillars

A geometric graph is a set of points in the plane (vertices) and a set of line segments between certain pairs of points (edges). A geometric graph is simple if the intersection of  two edges is empty or a vertex … Continue reading

Posted in Combinatorics, Geometry | Tagged , | 1 Comment

Touching Simplices and Polytopes: Perles’ argument

Joseph Zaks (1984), picture taken by Ludwig Danzer (OberWolfach photo collection)   The story I am going to tell here was told in several places, but it might be new to some readers and I will mention my own angle, … Continue reading

Posted in Combinatorics, Convex polytopes, Geometry, Open problems | Tagged , | Leave a comment

Proof By Lice!

From camels to lice. (A proof promised here.) Theorem (Hopf and Pannwitz, 1934): Let be a set of points in the plane  in general position (no three points on a line) and consider line segments whose endpoints are in .  Then … Continue reading

Posted in Combinatorics, What is Mathematics | Tagged | 7 Comments