2 citations · 4 across the 7 of their papers we have counts for
7 papers
A direct approach to the Gallai-Schur numbers
Fred Rowley
This paper characterises the structure of every maximal weak or strong Gallai-Schur partition. The results confirm the exact values of Gallai-Schur numbers provided by Budden (2020…
Improved Lower Bounds for Multicolour Ramsey Numbers using SAT-Solvers
Fred Rowley
This paper sets out the results of a range of searches for linear and cyclic graph colourings with specific Ramsey properties. The new graphs comprise mainly 'template graphs' whic…
An Improved Lower Bound for and Some Interesting Templates
Fred Rowley
In this simple paper, we exhibit a Schur partition giving rise to a triangle-free linear colouring of in 7 colours. Thus we show that the Schur number an…
New lower bounds for weak Schur partitions
Fred Rowley
This paper records some apparently new results for the partition of integer intervals [1, n] into weakly sum-free subsets. These were produced using a method closely related to tha…
A construction for weak Schur partitions
Fred Rowley
In 1952, J.H.Braun claimed to have established a formula giving a lower bound for certain partitions of sets of integers into weakly sum-free classes. However, no proof or supporti…
Some further results in Ramsey graph construction
Fred Rowley
A construction described by the current author (2017) uses two linear prototypes to build a compound graph with Ramsey properties inherited from the prototype graphs. The resulting…
A generalised linear Ramsey graph construction
Fred Rowley
A construction described by the current author in 2017 uses two linear `prototype' graphs to build a compound graph with Ramsey properties inherited from the prototypes. This paper…