10 papers
Logarithmic convergence of finite projective planes
Márton Borbényi, Panna TÃmea Fekete, Aranka HruÅ¡ková +1
In this paper, we study the so-called log-convergence of graphs defined by Balázs Szegedy (arXiv:1504.00858). We answer his Question 4 affirmatively: the sequence of incidence gra…
Fundamental cycles in grid graphs
BartÅomiej Kielak, Bartłomiej Kielak, Daniel Král' +3
We show that the average length of a fundamental cycle with respect to any fixed spanning tree of the square grid is at least ; the bound is asymptotically t…
Ramsey size linear and generalization
Eng Keat Hng, Meng Ji, Ander Lamaison
More than thirty years ago, ErdÅs, Faudree, Rousseau, and Schelp posed a fundamental question in extremal graph theory: What is the optimal constant such that $r(C_{2k+1}, G…
Spanning Components and Surfaces Under Minimum Vertex Degree
Jack Allsop, Ander Lamaison, Richard Lang +1
We study minimum vertex-degree conditions in 3-uniform hypergraphs for (tight) spanning components and (combinatorial) surfaces. Our main results show that a 3-uniform hypergraph $…
Hypergraphs with uniform Turán density equal to 8/27
Frederik Garbe, Daniel IľkoviÄ, Daniel Kráľ +2
In the 1980s, ErdÅs and Sós initiated the study of Turán problems with a uniformity condition on the distribution of edges: the uniform Turán density of a hypergraph is the…
Ramsey multiplicity of apices of trees
Daniel Kráľ, Matjaž Krnc, Ander Lamaison
A graph is common if its Ramsey multiplicity, i.e., the minimum number of monochromatic copies of contained in any -edge-coloring of , is asymptotically the same as…