3 citations · 6 across the 9 of their papers we have counts for
10 papers
Two-coloring cubic graphs with small monochromatic components, but without singletons
János Barát, Zoltán L. Blázsik
We combine two coloring aspects that work in opposite directions. One can 2-color the vertices of a cubic graph such that each monochromatic component is very small. One can also 2…
The double Hall property and cycle covers in bipartite graphs
János Barát, Andrzej Grzesik, Attila Jung +2
In a graph , the -neighborhood of a vertex set consists of all vertices of having at least neighbors in . We say that a bipartite graph satisfies the…
Improved upper bound on the Frank number of -edge-connected graphs
János Barát, Zoltán L. Blázsik
In an orientation of the graph , an arc is deletable if and only if is strongly connected. For a -edge-connected graph , the Frank number is the minimum …
General sharp upper bounds on the total coalition number
János Barát, Zoltán L. Blázsik
Let be a finite, simple, isolate-free graph. Two disjoint sets form a total coalition in , if none of them is a total dominating set, but their union $A\…
On the number of -transversals in hypergraphs
János Barát, Dániel Gerbner, Anastasia Halfpap
A set of vertices in a hypergraph is \textit{strongly independent} if every hyperedge shares at most one vertex with . We prove a sharp result for the number of maximal stro…
Monochromatic spanning trees and matchings in ordered complete graphs
János Barát, András Gyárfás, Géza Tóth
Two independent edges in ordered graphs can be nested, crossing or separated. These relations define six types of subgraphs, depending on which relations are forbidden. We refine a…
Quest for graphs of Frank number
János Barát, Zoltán L. Blázsik
In an orientation of the graph , the edge is deletable if and only if is strongly connected. For a -edge-connected graph , Hörsch and Szigeti defined the Fra…
The horizon of 2-dichromatic oriented graphs
János Barát, Mátyás Czett
The dichromatic number of a directed graph is at most 2, if we can 2-color the vertices such that each monochromatic part is acyclic. An oriented graph arises from a graph by orien…
Extremal -minor-free graphs without short cycles
János Barát
We determine the maximum number of edges in a -minor-free -vertex graph of girth , when or is even. We argue that there are many different -vertex extrema…
Saturated -planar drawings with few edges
János Barát, Géza Tóth
A drawing of a graph is -plane if every edge contains at most crossings. A -plane drawing is saturated if we cannot add any edge so that the drawing remains -plane. It…