Tiling $H$ in dense graphs
Combinatorics
2025-01-22 v1
Abstract
We determine asymptotically the two extremal constructions for the tiling problem of the -shaped tree. In particular, the first extremal construction is close to the complement of two cliques, in contrast to previously studied bipartite graphs, where the first extremal construction is close to the complement of a single clique. This result refutes one of Lang's conjectures [arXiv:2308.12281], which seeks to generalize the Erd\H{o}s Matching Conjecture.
Keywords
Cite
@article{arxiv.2501.11450,
title = {Tiling $H$ in dense graphs},
author = {Nannan Chen and Xizhi Liu and Lin Sun and Guanghui Wang},
journal= {arXiv preprint arXiv:2501.11450},
year = {2025}
}
Comments
45 pages, 64 figures, comments are welcome