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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…
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…
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…
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…