8 papers · 2 filters
Strict spectral supersaturation for cliques: extremal graphs and sharp thresholds
Qi Wu, Yong Lu
For every fixed and all sufficiently large , we determine the largest adjacency spectral radius of an -vertex graph with fewer than copies of , wh…
Exact random covers of metric trees: balanced rounding, duality, and sharp thresholds
Qi Wu, Yong Lu
Norin and Turcotte's asymptotically sharp bound for graph burning [J. Combin. Theory Ser. B 168 (2024), 208--235] led them to an exact random-cover conjecture for finite metric tre…
A Proof of the Chen--Raspaud Conjecture
Qi Wu, Yong Lu
For every integer , Chen and Raspaud conjectured that each graph with odd girth $\og(G)\ge2k+1$ and maximum average degree $\mad(G)<2+1/k$ has a -coloring. In…
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…
Hamiltonian cycles in 7-tough -free graphs
Yong Lu, Qi Wu, Qiannan Zhou
Shan~[J. Graph Theory (2026)] proved that every 23-tough -free graph on at least three vertices is Hamiltonian. We improve this bound to 7 by replacing the final cut…
Exact generalized Turán number of vertex-disjoint paths of length two
Qi Wu, Long-Tu Yuan
We determine the generalized Turán number of vertex-disjoint paths of length two and characterize all corresponding extremal graphs. Our proof combines the Lovász form of the Krusk…
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…
Triangles in graphs without the expansion of -cycle
Jialei Song, Qi Wu, Long-Tu Yuan
The expansion of a graph is the graph obtained from by replacing each edge with a triangle. Lv \etal proposed a conjecture on the maximum number of triangle…