9 papers
A Proof of the Erdős Matching Conjecture for Large Matchings via Sharp Tail Probability for Sums of i.i.d. Nonnegative Random Variables
Cheng Chi, Shuang Sun, Yan Wang
We resolve a conjecture of Łuczak, Mieczkowska and Šileikis on the maximal tail probability of sums of independent and identically distributed nonnegative random variables. Specifi…
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}…
On the structures of {diamond, bowtie}-free graphs that do not contain an induced subdivision of
Feng Liu, Shuang Sun, Yan Wang
A graph is -free if it contains no induced subdivision of . Lévêque et al. [\emph{J. Combin. Theory Ser. B} \textbf{102} (2012) 924--947] conjectured that all…
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…