On extremal colorings without rainbow cycles
Fragment książki (Abstrakt)
| Status: | |
| Autorzy: | Gorgol Izolda |
| Wersja dokumentu: | Elektroniczna |
| Język: | angielski |
| Strony: | 75 - 75 |
| Efekt badań statutowych | NIE |
| Materiał konferencyjny: | NIE |
| Publikacja OA: | NIE |
| Abstrakty: | angielski |
| While defining the anti-Ramsey number Erdős, Simonovits and Sós mentioned that the extremal colorings may not be unique [1]. In the talk we define ESS colorings to formalize colorings proposed by Erdős, Simonovits and Sós and characterize some of the extremal colorings avoiding rainbow cycles. In case of rainbow triangles, using ESS colorings, we fully characterize extremal Gallai colorings, that is Gallai colorings with maximum possible number of colors. Apart from that we show the recursive construction of such extremal Gallai colorings. It shows that the number of such colorings is equal to an appropriate Fibonacci number. By a double counting technique we obtain a new identity for Fibonacci numbers. |
