All missing Ramsey numbers for trees versus the four-page book
| Main Authors: | Lortz, Roland; Technische Universit\"at Braunschweig, Institut f\"ur Analysis und Algebra, AG Algebra 38092 Braunschweig, Germany, Mengersen, Ingrid; Moorh\"uttenweg 2d, 38104 Braunschweig, Germany |
|---|---|
| Other Authors: | Roland Lortz, Technische Universität Braunschweig, Institut für Analysis and Algebra, AG Algebra |
| Format: | Article info application/pdf eJournal |
| Bahasa: | eng |
| Terbitan: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB
, 2021
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| Subjects: | |
| Online Access: |
https://www.ejgta.org/index.php/ejgta/article/view/1092 https://www.ejgta.org/index.php/ejgta/article/view/1092/pdf_185 |
Daftar Isi:
- For the Ramsey number r(Tn, Bm), where Tn denotes a tree of order n and Bm denotes the m-page book K2 + bar(K)m, it is known that r(Tn, Bm)=2n − 1 if n ≥ 3m − 3. In case of n < 3m − 3, r(Tn, Bm) has not been completely evaluated except for m ≤ 3. Here we determine the missing values of r(Tn, B4). Our results close one gap in the table of the Ramsey numbers r(Tn, G) for all trees Tn and all connected graphs G of order six.