10 papers · 1 filter
Spread Methods for Induced Cycles
Lanchao Wang, Xiaolin Wang
We develop a spread-based approach to finding induced cycles and apply it to two problems. First, we resolve the odd-hole gadget conjecture of Bradač, Draganić and Sudakov by const…
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…