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math.CO2026
Optimal and Near-Optimal Constructions for Bootstrap Percolation in Hypercubes
Jonathan A. Noel
The -neighbour bootstrap process on a graph begins with a set of infected vertices; subsequently, healthy vertices become infected once they have at least infected neigh…
math.CO2025
Maximizing Alternating Paths via Entropy
Hao Chen, Felix Christian Clemen, Jonathan A. Noel
We prove that if is an -vertex graph whose edges are coloured with red and blue, then the number of colour-alternating walks of length with red edges and bl…
math.CO2025
On Alternating 6-Cycles in Edge-Coloured Graphs
Hao Chen, Jonathan A. Noel
In this short note, we use flag algebras to prove that the number of colour alternating 6-cycles in a red/blue colouring of a large clique is asymptotically maximized by a uniforml…