𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Proof of a conjecture of Burr, Grünbaum, and Sloane

✍ Scribed by Jacob E. Goodman

Publisher
Elsevier Science
Year
1980
Tongue
English
Weight
926 KB
Volume
32
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

We establish a duality principle for arrangements of pseudolines in the projective plane, and thereby prove the conjecture of Burr, Griinbaum, and Sloane that the solution T(p) of the "orchard problem" for pseudoline arrangements and the solution r(p) of the dual problem xe equa1.

📜 SIMILAR VOLUMES

A conjecture of Borodin and a coloring o
A conjecture of Borodin and a coloring of Grünbaum
✍ Dieter Rautenbach 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 114 KB

## Abstract In 1976, Borodin conjectured that every planar graph has a 5‐coloring such that the union of every __k__ color classes with 1 ≤ __k__ ≤ 4 induces a (__k__—1)‐degenerate graph. We prove the existence of such a coloring using 18 colors. © 2008 Wiley Periodicals, Inc. J Graph Theory 58:139

A new proof of Grünbaum's 3 color theore
A new proof of Grünbaum's 3 color theorem
✍ O.V. Borodin 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 307 KB

A simple proof of Grfinbaum's theorem on the 3-colourability of planar graphs having at most three 3-cycles is given, which does not employ the colouring extension. In 1958, Gr6tzsch I-5] proved that every planar graph without cycles of length three is 3-colourable. In 1963, Griinbaum [6] extended

Proof of a Conjecture of Frankl and Füre
Proof of a Conjecture of Frankl and Füredi
✍ Gurumurthi V. Ramanan 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 375 KB

We give a simple linear algebraic proof of the following conjecture of Frankl and Fu redi [7,9,13]. (Frankl We generalise a method of Palisse and our proof-technique can be viewed as a variant of the technique used by Tverberg to prove a result of Graham and Pollak [10,11,14]. Our proof-technique