12 papers · 1 filter
Compactness of abundance in asymmetric hypergraph removal lemmas
Shuang Sun, Yan Wang, Yuyao Yang +1
Fix an integer and a finite simple -uniform hypergraph with at least one edge and no isolated vertices. An -vertex -graph is -far from being -free if at…
Asymptotic Uniformity of Permanents of Random Matrices over Finite Fields of Odd Characteristic
Shuang Sun, Yuyao Yang, Jiasheng Zeng
Let be an odd prime power, and let be a random matrix whose entries are independent and uniformly distributed on . The per…
Every fork-free graph is perfectly weight divisible
Feng Liu, Shuang Sun, Yan Wang +2
A graph is \emph{perfectly weight divisible} if, for every positive integral weight function on and every induced subgraph of with at least one edge, the vertex…
A Single-Exponential Erdős--Hajnal Bound for Graphs of Bounded VC-Dimension
Shuang Sun, Yan Wang, Jiasheng Zeng
A homogeneous set in a graph is a clique or a stable set. The Erdős--Hajnal conjecture states that, for every graph , there exists such that every -free graph on ve…
Finite-Kernel Extremizers in Sparse Extremal Graph Counting
Jiasheng Zeng
We develop a finite-kernel framework for sparse extremal graph counting. The problems considered here ask for the maximum number of copies or homomorphisms of a fixed graph under s…
Proofs of Two Conjectures of Alon on Subgraph Counts
Peiru Kuang, Shuang Sun, Yan Wang +1
All graphs considered are finite with no isolated vertices. Let be the maximum number of subgraphs of a graph isomorphic to , taken over all graphs with edg…
Sharp Bounds for Guiduli-Type Hereditary Spectral Problems
Dongxiu Cai, Jiasheng Zeng, Xiao-Dong Zhang
Guiduli asked in 1996 the following problem concerning the maximum spectral radius of a graph under hereditary density constraints. If an -vertex graph satisfies $e(H)\le c|…
Tight Bound for Nikiforov's Spectral Even-Cycle Conjecture
Peiru Kuang, Feng Liu, Shuang Sun +2
Nikiforov conjectured that, for every fixed and all sufficiently large , the unique -vertex -free graph with maximum adjacency spectral radius is $S^+_{n,k}…
Polylogarithmic Bounds for Nested Cycles without Geometric Crossings
Yue Xu, Jiasheng Zeng, Xiao-Dong Zhang
A problem of Erdős asks for extremal conditions forcing edge-disjoint cycles with a prescribed nested structure. In the geometric version, the nesting is required to be noncrossing…
A note on the -partite link problem of Füredi
Jianfeng Hou, Xinmin Hou, Xizhi Liu +2
Motivated by the Erdős--Sós bipartite link conjecture, Füredi (Oberwolfach, 2004) asked for the asymptotic maximum edge density of -graphs in which the li…
On the -problem of Brown, Erdős and Sós for even integers
Yan Wang, Jiasheng Zeng
Let denote the maximum number of edges in an -graph on vertices in which every edges span more than vertices. Brown, Erdős and Sós in 1973 conjectur…
On the Borodin--Kostochka conjecture for graphs with large maximum degree
Feng Liu, Shuang Sun, Yan Wang +1
The Borodin--Kostochka conjecture states that every graph with maximum degree satisfies . In this paper, we verify this conjecture for…