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Two conjectures of Grünbaum on arrangements of curves

✍ Scribed by Pierre Masai


Book ID
107748418
Publisher
Elsevier Science
Year
1982
Tongue
English
Weight
794 KB
Volume
41
Category
Article
ISSN
0012-365X

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Proof of a conjecture of Burr, Grünbaum,
✍ Jacob E. Goodman 📂 Article 📅 1980 🏛 Elsevier Science 🌐 English ⚖ 926 KB

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.

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✍ 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