16 citations · 67 across the 17 of their papers we have counts for
18 papers
An automated proof that R(B_8,B_10)=37
Jeremy Kalfus, Bernard Lidický
We present a short proof that the book Ramsey number equals 37. The lower bound is already available in the literature, so it is enough to ru…
Planar Turán Numbers of Cycles: A Counterexample
Daniel W. Cranston, Bernard Lidický, Xiaonan Liu +1
The planar Turan number is the largest number of edges in an -vertex planar graph with no -cycle. For , upper…
Solving Turán's Tetrahedron Problem for the -Norm
József Balogh, Felix Christian Clemen, Bernard Lidický
Turán's famous tetrahedron problem is to compute the Turán density of the tetrahedron . This is equivalent to determining the maximum -norm of the codegree vector of…
Max Cuts in Triangle-free Graphs
József Balogh, Felix Christian Clemen, Bernard Lidický
A well-known conjecture by Erdős states that every triangle-free graph on vertices can be made bipartite by removing at most edges. This conjecture was known for graph…
Inducibility of 4-vertex tournaments
Dalton Burke, Bernard Lidický, Florian Pfender +1
We determine the inducibility of all tournaments with at most vertices together with the extremal constructions. The -vertex tournament containing an oriented and one…
is almost a fractalizer
Bernard Lidický, Connor Mattes, Florian Pfender
We determine the maximum number of induced copies of a 5-cycle in a graph on vertices for every . Every extremal construction is a balanced iterated blow-up of the 5-cycle w…
Maximum Number of Almost Similar Triangles in the Plane
József Balogh, Felix Christian Clemen, Bernard Lidický
A triangle is -similar to another triangle if their angles pairwise differ by at most . Given a triangle , and $n\in\mathbb{N}…
On tripartite common graphs
Andrzej Grzesik, Joonkyung Lee, Bernard Lidický +1
A graph H is common if the number of monochromatic copies of H in a 2-edge-colouring of the complete graph is minimised by the random colouring. Burr and Rosta, extending a famous…
Hadamard diagonalizable graphs of order at most 36
Jane Breen, Steve Butler, Melissa Fuentes +7
If the Laplacian matrix of a graph has a full set of orthogonal eigenvectors with entries , then the matrix formed by taking the columns as the eigenvectors is a Hadamard mat…
Making -Free Graphs -partite
József Balogh, Felix Christian Clemen, Mikhail Lavrov +2
The Erdős-Simonovits stability theorem states that for all ε>0 there exists α>0 such that if G is a K_{r+1}-free graph on n vertices with e(G) > ex(n,K_{r+1}) - αn^2, then one can…
Sharp bounds for decomposing graphs into edges and triangles
Adam Blumenthal, Bernard Lidický, Yanitsa Pehova +3
For a real constant , let be the minimum of twice the number of 's plus times the number of 's over all edge decompositions of into copies of …
Coloring count cones of planar graphs
Zdeněk Dvořák, Bernard Lidický
For a plane near-triangulation with the outer face bounded by a cycle , let denote the function that to each -coloring of assigns the number of ways $…
Inducibility of directed paths
Ilkyoo Choi, Bernard Lidický, Florian Pfender
A long standing open problem in extremal graph theory is to describe all graphs that maximize the number of induced copies of a path on four vertices. The character of the problem…
Minimizing the number of 5-cycles in graphs with given edge-density
Patrick Bennett, Andrzej Dudek, Bernard Lidický +1
Motivated by the work of Razborov about the minimal density of triangles in graphs we study the minimal density of the 5-cycle . We show that every graph of order and size…
Semidefinite Programming and Ramsey Numbers
Bernard Lidický, Florian Pfender
Finding exact Ramsey numbers is a problem typically restricted to relatively small graphs. The flag algebra method was developed to find asymptotic results for very large graphs, s…
Polychromatic Colorings on the Integers
Maria Axenovich, John Goldwasser, Bernard Lidický +4
We show that for any set , there exists a 3-coloring of in which every translate of receives all three colors. This implies that …
Ore and Chvátal-type Degree Conditions for Bootstrap Percolation from Small Sets
Michael Dairyko, Michael Ferrara, Bernard Lidický +3
Bootstrap percolation is a deterministic cellular automaton in which vertices of a graph~ begin in one of two states, "dormant" or "active". Given a fixed integer , a dormant…
Polychromatic Colorings on the Hypercube
John Goldwasser, Bernard Lidický, Ryan R. Martin +3
Given a subgraph G of the hypercube Q_n, a coloring of the edges of Q_n such that every embedding of G contains an edge of every color is called a G-polychromatic coloring. The max…