6 papers
Set-defined graph classes: -boundedness meets tropical algebra
Sarosh Adenwalla, Samuel Braunfeld, Tomáš Hons +2
We study set-defined graph classes: hereditary classes whose vertices are assigned fixed-length numerical tuples, with adjacency determined solely by equality patterns among coordi…
On a Generalisation of a Function of Ron Graham's
Sarosh Adenwalla
Ron Graham introduced a function, , on the non-negative integers, in the 1986 Issue Problems column of \textit{Mathematical Magazine}: For each non-negative integer ,…
A Question of Erdős and Graham on Covering Systems
Sarosh Adenwalla
Erdős and Graham (Erdős and Graham, 1980) asked if there exists an such that the divisors of greater than 1 are the moduli of a distinct covering system with the following…
Boolean combinations of graphs
Sarosh Adenwalla, Samuel Braunfeld, John Sylvester +1
Boolean combinations allow combining given combinatorial objects to obtain new, potentially more complicated, objects. In this paper, we initiate a systematic study of this idea ap…
A Generalisation of a Result on Monotone Arithmetic Progressions in Permutations of the Positive Integers
Sarosh Adenwalla
A permutation of the positive integers avoiding monotone arithmetic progressions of length with odd common difference was constructed in (LeSaulnier and Vijay, 2011). We genera…
Avoiding Monotone Arithmetic Progressions in Permutations of Integers
Sarosh Adenwalla
A permutation of the integers avoiding monotone arithmetic progressions of length was constructed in (Geneson, 2018). We improve on this by constructing a permutation of the in…