58 citations · 549 across the 45 of their papers we have counts for
6 papers · 2 filters
Pentagons in triangle-free graphs
Bernard Lidický, Florian Pfender
For all , we show that the only triangle-free graphs on vertices maximizing the number -cycles are balanced blow-ups of a 5-cycle. This completely resolves a conject…
Closing in on Hill's conjecture
József Balogh, Bernard Lidický, Gelasio Salazar
Borrowing László Székely's lively expression, we show that Hill's conjecture is "asymptotically at least 98.5% true". This long-standing conjecture states that the crossing number…
Decomposing graphs into edges and triangles
Daniel Král', Bernard Lidický, Taísa L. Martins +1
We prove the following 30-year old conjecture of Győri and Tuza: the edges of every -vertex graph can be decomposed into complete graphs of orders two an…
3-coloring triangle-free planar graphs with a precolored 9-cycle
Ilkyoo Choi, Jan Ekstein, Přemysl Holub +1
Given a triangle-free planar graph G and a 9-cycle C in G, we characterize situations where a 3-coloring of C does not extend to a proper 3-coloring of G. This extends previous res…
A counterexample to a conjecture on facial unique-maximal colorings
Bernard Lidický, Kacy Messerschmidt, Riste Škrekovski
A facial unique-maximum coloring of a plane graph is a proper vertex coloring by natural numbers where on each face the maximal color appears exactly once on the vertices of $α…
On facial unique-maximum (edge-)coloring
Vesna Andova, Bernard Lidický, Borut Lužar +1
A facial unique-maximum coloring of a plane graph is a vertex coloring where on each face the maximal color appears exactly once on the vertices of . If the coloring is requ…