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Tiling H in dense graphs

2025/01/20 by Xizhi Liu, Chen, Nannan, Liu, Xizhi +4 · 1 citation
Mathematics · Engineering · Computer Science · #Graph theory and applications #graph theory and CDMA systems #Advanced Graph Theory Research

paper · pdf · doi:10.48550/arxiv.2501.11450

Abstract

We determine asymptotically the two extremal constructions for the tiling problem of the H-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 Erdős Matching Conjecture.

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