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Triangle-Free Geometric Intersection Graphs with Large Chromatic Number

✍ Scribed by Pawlik, Arkadiusz; Kozik, Jakub; Krawczyk, Tomasz; Lasoń, Michał; Micek, Piotr; Trotter, William T.; Walczak, Bartosz

Book ID
121622827
Publisher
Springer
Year
2013
Tongue
English
Weight
296 KB
Volume
50
Category
Article
ISSN
0179-5376

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A triangle-free circle graph with chroma
A triangle-free circle graph with chromatic number 5
✍ A.A. Ageev 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 170 KB

It follows from the results of , Gyirfis and Lehel (1985), and Kostochka (1988) that 4 ~x\* ## ~5 where x\* = max {X(G): G is a triangle-free circle graph}. We show that X\* ? 5 and thus X\* = 5. This disproves the conjecture of Karapetyan that X\* = 4 and answers negatively a question of Gyirfis