We provide an optimal sufficient condition, relating minimum degree and bandwidth, for a graph to contain a spanning subdivision of the complete bipartite graph K2,ℓ. This includes the containment of Hamilton paths and cycles, and has applications in the random geometric graph model. Our proof provides a greedy algorithm for constructing such structures.
@article{arxiv.2407.05889,
title = {Dirac's theorem for graphs of bounded bandwidth},
author = {Alberto Espuny Díaz and Pranshu Gupta and Domenico Mergoni Cecchelli and Olaf Parczyk and Amedeo Sgueglia},
journal= {arXiv preprint arXiv:2407.05889},
year = {2026}
}