9 papers · 1 filter
Induced Size-Ramsey Numbers of Odd Cycles via Spread Measures
Lanchao Wang, Xiaolin Wang
We prove that, for every and every sufficiently large odd , the induced size--Ramsey number of satisfies \[ \widehat R_{\mathrm{ind}}(C_n;k)=e^{Θ(k)}n. \] This imp…
Prescribed-order subdigraphs with large minimum out-degree
Bin Chen, Lanchao Wang
Alon introduced as the largest integer such that every digraph on vertices with minimum out-degree at least contains a subdigraph on vertices with minimum o…
Superlinear Lower Bounds for Monochromatic Path Partitions
Heng Li, Lanchao Wang
In 1989, Gyárfás conjectured that the vertex set of every -edge-coloured complete graph can be partitioned into at most vertex-disjoint monochromatic paths. Erdős, Gyárfás,…
The Turán number of the Cartesian product of trees via star-flip
Lanchao Wang, Caihong Yang
Motivated by Erdős's conjecture on the Turán number of degenerate bipartite graphs, Bradač, Janzer, Sudakov and Tomon proved that $ \ex(n,T \Box P)=Θ_{T,P}(n^{3/2})$ for every nont…
Tight Staircase Bounds for Cyclic Subsets below Dirac's Threshold
Hong Liu, Mengyuan Niu, Lanchao Wang +1
Let denote the number of cyclic subsets in a graph , which are subsets that induce a Hamiltonian subgraph. Draganić, Keevash and Müyesser recently proved…
An exact robust Ramsey theorem for matchings
Mengyuan Niu, Lanchao Wang
Keevash and Michaeli recently proved that, under the robustness assumption that \(G\) is an \(s\)-connector (i.e. \(\overline G\) is \(K_{s,s}\)-free), \(G\) has essentially the sa…
Constructor--Blocker games forbidding even cycles
Lanchao Wang, Zhifei Yan
The Constructor--Blocker game is played on the edge set of . Two players alternately claim previously unclaimed edges. Constructor aims to maximize the number of copies of a t…
Structural Reductions for Monochromatic Matchings and Ramsey Tilings
Hong Liu, Maksim Turevskii, Lanchao Wang +1
The Alon--Frankl--Lovász theorem determines the chromatic number of Kneser hypergraphs; equivalently, it gives the sharp minimum size of a monochromatic matching in every edge-colo…
Triangle packings in randomly perturbed graphs
Xinbu Cheng, Hong Liu, Lanchao Wang +1
The longstanding Nash-Williams conjecture asserts that every -divisible graph with admits a triangle decomposition. In the random setting, Frankl and Rödl s…