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math.CO2026
On Ramsey-type problems for paths and cycles with few colour changes
Peter Allen, Julia Böttcher, Dennis Clemens +3
In 1967, Gerencser and Gyárfás determined the exact values of the two-colour Ramsey numbers of paths. In a footnote, they made the following observation: Every -edge-coloured co…
math.CO2026
The density of graphs with no -path connecting equal-degree vertices: a short proof
Yamaan Attwa, Matías Azócar Carvajal, Simona Boyadzhiyska +2
Addressing a question posed by Chen and Ma from an asymptotic point of view, we present a short proof for the edge density needed to guarantee that two vertices of the same degree…