Publications (38)
Properly colored and rainbow copies of graphs with few cherries
Benny Sudakov, Jan Volec
Let G be an n-vertex graph that contains linearly many cherries (i.e., paths on 3 vertices), and let c be a coloring of the edges of the complete graph K_n such that at each vertex…
A bound on the inducibility of cycles
Daniel Kral, Sergey Norin, Jan Volec
In 1975, Pippenger and Golumbic conjectured that every n-vertex graph has at most induced cycles of length k for k at least 5. We prove that every n-vertex graph ha…
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…
Compactness and finite forcibility of graphons
Roman Glebov, Daniel Kral, Jan Volec
Graphons are analytic objects associated with convergent sequences of graphs. Problems from extremal combinatorics and theoretical computer science led to a study of graphons deter…
The Spectrum of Triangle-free Graphs
József Balogh, Felix Christian Clemen, Bernard Lidický +2
Denote by the smallest eigenvalue of the signless Laplacian matrix of an -vertex graph . Brandt conjectured in 1997 that for regular triangle-free graphs $q_n(G) \le…
Towards characterizing locally common graphs
Robert Hancock, Daniel Kral, Matjaz Krnc +1
A graph H is common if the number of monochromatic copies of H in a 2-edge-coloring of the complete graph is asymptotically minimized by the random coloring. The classification of…