35 citations · 94 across the 13 of their papers we have counts for
15 papers
A cube dismantling problem related to bootstrap percolation
János Barát, Ian M. Wanless
An hypercube is made from unit hypercubes. Two unit hypercubes are neighbours if they share a -dimensional face. In each step of a disma…
Decomposition of cubic graphs related to Wegner's conjecture
János Barát
Thomassen formulated the following conjecture: Every -connected cubic graph has a red-blue vertex coloring such that the blue subgraph has maximum degree (that is, it consis…
Transversals in generalized Latin squares
János Barát, Zoltán Lóránt Nagy
We are seeking a sufficient condition that forces a transversal in a generalized Latin square. A generalized Latin square of order is equivalent to a proper edge-coloring of $K…
A family of extremal hypergraphs for Ryser's conjecture
Ahmad Abu-Khazneh, János Barát, Alexey Pokrovskiy +1
Ryser's Conjecture states that for any -partite -uniform hypergraph, the vertex cover number is at most times the matching number. This conjecture is only known to be…
Improvements on the density of maximal 1-planar graphs
János Barát, Géza Tóth
A graph is 1-planar if it can be drawn in the plane such that each edge is crossed at most once. A graph, together with a 1-planar drawing is called 1-plane. Brandenburg et al. sho…
Partitioning 2-edge-colored graphs by monochromatic paths and cycles
Jozsef Balogh, Janos Barat, Daniel Gerbner +2
We present results on partitioning the vertices of -edge-colored graphs into monochromatic paths and cycles. We prove asymptotically the two-color case of a conjecture of Sárköz…