8 papers
Maximum spread of -minor-free graphs II: the non-admissible cases
William Linz, Linyuan Lu, Zhiyu Wang
We have previously determined the maximum-spread -minor-free graph(s) on vertices when is sufficiently large, , and or $t\ge \frac{3}{2}(s-3) +…
Generalized Nordhaus--Gaddum Inequalities for Eigenvalues
Sahil Agarwal, Carter Antley, Joseph Aulenbacher +6
For a graph , let denote the adjacency eigenvalues of . We investigate the asymptotic maximum of \[ λ_i(G)+λ_j(\overline G) \] f…
Turán-Type Bounds for Graphs Containing Large -Sparse Sets
Yupei Li, Linyuan Lu
We study Turán-type extremal problems for graphs containing a large -sparse vertex set, meaning a vertex set whose induced subgraph contains few copies of . For integers $r>…
Maximum spectral gaps of graphs
George Brooks, William Linz, Linyuan Lu
The spread of a graph is the difference between the largest and smallest eigenvalues of its adjacency matrix. Breen, Riasanovsky, Tait and Urschel recently determ…
An Ore-type theorem for -graphs
Yupei Li, Linyuan Lu, Ruth Luo
Ore's Theorem states that if is an -vertex graph and every pair of non-adjacent vertices has degree sum at least , then is Hamiltonian. A -graph is a hypergraph…
Maximum spread of -minor-free graphs
William Linz, Linyuan Lu, Zhiyu Wang
The spread of a graph is the difference between the largest and smallest eigenvalue of the adjacency matrix of . In this paper, we consider the family of graphs which contai…