10 papers · 1 filter
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…
Tight Hamiltonian Cycles in Uniformly Dense -Graphs
Yaobin Chen, Jie Han, Xizhi Liu
We study minimum degree conditions for tight Hamiltonian cycles in uniformly dense -uniform hypergraphs. We prove that for every , every sufficiently large -dense…
Upper Bounds on Turán Densities via Extremal Set Theory
Yaobin Chen, Xizhi Liu, Ningyuan Yang +1
We exhibit, in a systematic way, connections between hypergraph Turán problems and extremal set theory. More specifically, we construct natural families of uniform hypergraphs for…
Hitting time for Hamilton cycles in pseudorandom graphs
Yaobin Chen, Yu Chen, Seonghyuk Im +1
Consider the random subgraph process on a base graph with vertices: we generate a sequence by taking a uniformly random ordering of the edges of $G…
Note on the trace of random walks on pseudorandom graphs
Yaobin Chen, Yiting Wang
We study the graph-theoretic properties of the trace of random walks on pseudorandom graphs. We show that for any , there exists a constant such that the cover t…
Robustness for expander graphs
Yaobin Chen, Yu Chen, Jie Han +1
We study robust versions of properties of -graphs, namely, the property of a random sparsification of an -graph, where each edge is retained with probability …
Unbounded degree spanning hypertrees in Dirac hypergraphs
Yaobin Chen, Seonghyuk Im, Junchi Zhang
In 2001, Komlós, Sárközy, and Szemerédi proved that every sufficiently large -vertex graph with minimum degree at least contains all spanning trees with ma…
Limit for Quotient Convergent Graph Sequence
Yaobin Chen, Zhicheng Liu, Yihang Xiao +1
Building on the limit theory for set functions, we prove that the limit of convergent sequence of bounded-degree graphs' cycle matroids can be represented as the cycle matroid of a…
Embedding loose trees in -uniform hypergraphs
Yaobin Chen, Allan Lo
A classical result of Komlós, Sárközy and Szemerédi shows that every large -vertex graph with minimum degree at least contains all spanning trees of bounded degree. W…