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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Ingrid Mengersen
Moorh\"uttenweg 2d, 38104 Braunschweig, Germany
Electrical & Electronics Engineering

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All missing Ramsey numbers for trees versus the four-page book Roland Lortz; Ingrid Mengersen
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.2.10

Abstract

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.
Co-Authors Roland Lortz