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On minimal triangle-free graphs with prescribed -defective chromatic number

✍ Scribed by Nirmala Achuthan; N.R. Achuthan; M. Simanihuruk

Book ID
108114264
Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
516 KB
Volume
311
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES

On minimal 5-chromatic triangle-free gra
On minimal 5-chromatic triangle-free graphs
✍ David Avis πŸ“‚ Article πŸ“… 1979 πŸ› John Wiley and Sons 🌐 English βš– 139 KB πŸ‘ 1 views

## Abstract It is shown that the minimum number of vertices in a triangle‐free 5‐chromatic graph is at least 19.

A triangle-free circle graph with chroma
A triangle-free circle graph with chromatic number 5
✍ A.A. Ageev πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 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