7 papers
The 2-Adic Valuation of the Order of the All-Ones Class in the Sandpile Group of a Square
Turgay Akyar, Artem Beliakov, Konstantin Delchev +6
Place one grain at every nonsink vertex of the wired square, and let be the order of this operation in the sandpile group. Thus is the least positive …
Weak saturation of tensor product of cliques
Nikolai Terekhov
Given two hypergraphs and , the weak saturation number is the minimum number of edges in a spanning subhypergraph of such that th…
Asymptotically optimal lower bounds on weak saturation numbers for hypergraphs
Nikolai Terekhov
Given an -uniform hypergraph and a positive integer , the weak saturation number is the minimum number of edges in an -uniform hypergraph on $…
Forbidding just one intersection for short integer sequences
Elizaveta Iarovikova, Fedor Noskov, Georgy Sokolov +1
In this paper, we study the famous Erdős--Sós forbidden intersection problem for words over an alphabet of size : what is the maximal size of a subfamily of $[m]^n…
A short proof of Tuza's conjecture for weak saturation in hypergraphs
Nikolai Terekhov
Given an -uniform hypergraph and a positive integer , the weak saturation number is the minimum number of edges in an -uniform hypergraph on $…
Weak saturation rank: a failure of linear algebraic approach to weak saturation
Nikolai Terekhov, Maksim Zhukovskii
Given a graph and a positive integer , the weak -saturation number is the minimum number of edges in a graph on vertices such that the edge…
Weak saturation in graphs: a combinatorial approach
Nikolai Terekhov, Maksim Zhukovskii
The weak saturation number is the minimum number of edges in a graph on vertices such that all the missing edges can be activated sequentially so that each…