7 papers
On -factors of Hamiltonian graphs
Alberto Espuny Díaz, António Girão, Bertille Granet +1
Let . We show that, for a sufficiently small , any sufficiently large -vertex Hamiltonian graph of minimum degree at least contains a…
On constructing small subgraphs in the budget-constrained random graph process
Sylwia Antoniuk, Alberto Espuny Díaz, Kalina Petrova +1
Consider the budget-constrained random graph process introduced by Frieze, Krivelevich and Michaeli, where each time an edge is offered through the (standard) random graph process…
Graph factors and powers of Hamilton cycles in the budget-constrained random graph process
Alberto Espuny Díaz, Frederik Garbe, Tássio Naia +1
We consider the following budget-constrained random graph process introduced by Frieze, Krivelevich and Michaeli. A player, called Builder, is presented with distinct edges of…
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…