8 papers
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…
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…
Optimal coloring of -free graphs with no short odd holes
Feng Liu, Shuang Sun, Yan Wang
A \emph{hole} is an induced cycle of length at least four, and an \emph{even hole} is a hole of even length. A \emph{cap} is obtained from a hole by adding a vertex adjacent to exa…
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…
Local Turán inequalities for walks and the spectral radius
Feng Liu, Shuang Sun, Yan Wang +1
Nikiforov's well-known spectral Turán inequality for walks states that, for every graph with clique number , , where is the largest eig…
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}…