4 papers · 1 filter
Exponential odd-distance sets under the Manhattan metric
Alberto Espuny Díaz, Emma Hogan, Freddie Illingworth +3
We construct a set of points in such that all pairwise Manhattan distances are odd integers, which improves the recent linear lower bound of Golovanov, Kupavsk…
How many random edges make an almost-Dirac graph Hamiltonian?
Alberto Espuny Díaz, Richarlotte Valérà Razafindravola
We study Hamiltonicity in the union of an -vertex graph with high minimum degree and a binomial random graph on the same vertex set. In particular, we consider the case when…
Dirac's theorem for graphs of bounded bandwidth
Alberto Espuny Díaz, Pranshu Gupta, Domenico Mergoni Cecchelli +2
We provide an optimal sufficient condition, relating minimum degree and bandwidth, for a graph to contain a spanning subdivision of the complete bipartite graph . This…
On the local resilience of random geometric graphs with respect to connectivity and long cycles
Alberto Espuny Díaz, Lyuben Lichev, Alexandra Wesolek
Given an increasing graph property , a graph is -resilient with respect to if, for every spanning subgraph where each vertex keeps…