7 papers
Graph factors and powers of Hamilton cycles in the budget-constrained random graph process
Alberto Espuny DÃaz, 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…
On -factors of Hamiltonian graphs
Alberto Espuny DÃaz, 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 DÃaz, 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…
Exponential odd-distance sets under the Manhattan metric
Alberto Espuny DÃaz, 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 DÃaz, 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 DÃaz, 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…