8 papers
The Erdős-Gallai bound for consecutive even cycle lengths
Yaobin Chen, Hong Liu, Xia Wang +2
Erdős and Gallai in 1959 proved the seminal result that every -vertex graph with no cycle of length at least has at most edges. We prove the extens…
Small circumference in regular sublinear expanders
Yaobin Chen, Hong Liu, Xin Wei +1
Sublinear expansion is weak enough to be extracted from arbitrary graphs while retaining nearly all of their average degree, yet it has proved strong enough to force global structu…
Large cliques in graphs with forbidden semi-induced structures
Nannan Chen, Yulai Ma, Fan Yang
In 2022, Holmsen showed that any graph with at least \( c \binom{n}{r} \) \(r\)-cliques but no induced complete -partite graph must contain a clique of order \…
Topological cliques in sparse expanders
Xia Wang, Donglei Yang, Fan Yang +1
In the paper, we focus on embedding clique immersions and subdivisions within sparse expanders, and we derive the following main results: (1) For any , there exists $K>0…
Balanced clique subdivisions and cycles lengths in -free graphs
Jianfeng Hou, Yindong Jin, Donglei Yang +1
Let be integers. Confirming a conjecture of Mader, Liu and Montgomery [J. Lond. Math. Soc., 2017] showed that every -free graph with average degree cont…
Embedding clique subdivisions via crux
Donglei Yang, Fan Yang
For a graph and a constant , we denote by the minimum order of a subgraph with . Liu and Montgomery conjectured that every graph …
A Hypergraph Approach to Distributed Broadcast
Qi Cao, Yulin Shao, Fan Yang +1
This paper explores the distributed broadcast problem within the context of network communications, a critical challenge in decentralized information dissemination. We put forth a…
Extremal density for subdivisions with length or sparsity constraints
Jaehoon Kim, Hong Liu, Yantao Tang +3
Given a graph , a balanced subdivision of is obtained by replacing all edges of with internally disjoint paths of the same length. In this paper, we prove that for any g…