16 citations · 53 across the 13 of their papers we have counts for
18 papers
Minimally tough series-parallel graphs with toughness at least
Gyula Y. Katona, Humara Khan
Let be a positive real number. A graph is called \emph{-tough} if the removal of any vertex set that disconnects the graph leaves at most components. The toughne…
Towards a Baranyai theorem with additional condition
Gyula O. H. Katona, Gyula Y. Katona
A partial partition of an -element set is a collection of pairwise disjoint -element subsets. It is proved that, if is large enough, one can find $\le…
On minimally tough chordal graphs
Clément Dallard, Blas Fernández, Gyula Y. Katona +2
Katona and Varga showed that for any rational number , no chordal graph is minimally -tough, while Katona and Khan characterized all minimally -tough, chordal…
Minimally tough chordal graphs with toughness at most
Gyula Y. Katona, Humara Khan
Let be a positive real number. A graph is called \emph{-tough} if the removal of any vertex set that disconnects the graph leaves at most components. The toughne…
Strengthening some complexity results on toughness of graphs
Gyula Y Katona, Kitti Varga
Let be a positive real number. A graph is called -tough if the removal of any vertex set that disconnects the graph leaves at most components. The toughness of a…
Optimal pebbling number of the square grid
Ervin Győri, Gyula Y. Katona, László F. Papp
A pebbling move on a graph removes two pebbles from a vertex and adds one pebble to an adjacent vertex. A vertex is reachable from a pebble distribution if it is possible to move a…
Optimal pebbling number of graphs with given minimum degree
Andrzej Czygrinow, Glenn Hurlbert, Gyula Y. Katona +1
Consider a distribution of pebbles on a connected graph . A pebbling move removes two pebbles from a vertex and places one to an adjacent vertex. A vertex is reachable under a p…
Decomposition of a graph into two disjoint odd subgraphs
Mikio Kano, Gyula Y. Katona, Kitti Varga
An odd (resp. even) subgraph in a multigraph is its subgraph in which every vertex has odd (resp. even) degree. We say that a multigraph can be decomposed into two odd subgraphs if…
Minimal toughness in special graph classes
Gyula Y. Katona, Kitti Varga
Let be a positive real number. A graph is called -tough if the removal of any vertex set that disconnects the graph leaves at most components, and all graphs are…
Optimal pebbling and rubbling of graphs with given diameter
Ervin Győri, Gyula Y. Katona, László F. Papp
A pebbling move on a graph removes two pebbles from a vertex and adds one pebble to an adjacent vertex. A vertex is reachable from a pebble distribution if it is possible to move a…
The complexity of recognizing minimally tough graphs
Gyula Y Katona, István Kovács, Kitti Varga
A graph is called -tough if the removal of any vertex set that disconnects the graph leaves at most components. The toughness of a graph is the largest for which…
The Optimal Pebbling Number of Staircase Graphs
Ervin Győri, Gyula Y. Katona, László F. Papp +1
Let G be a graph with a distribution of pebbles on its vertices. A pebbling move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The…
Properties of minimally -tough graphs
Gyula Y. Katona, Dániel Soltész, Kitti Varga
A graph is minimally -tough if the toughness of is and the deletion of any edge from decreases the toughness. Kriesell conjectured that for every minimally -t…
Constructions for the optimal pebbling of grids
Ervin Győri, Gyula Y. Katona, László F. Papp
In [C. Xue, C. Yerger: Optimal Pebbling on Grids, Graphs and Combinatorics] the authors conjecture that if every vertex of an infinite square grid is reachable from a pebble distri…
SIS epidemic propagation on hypergraphs
Ágnes Bodó, Gyula Y. Katona, Péter L. Simon
Mathematical modeling of epidemic propagation on networks is extended to hypergraphs in order to account for both the community structure and the nonlinear dependence of the infect…
The Optimal Rubbling Number of Ladders, Prisms and Möbius-ladders
Gyula Y. Katona, László F. Papp
A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this…
Bounds on the Number of Edges in Hypertrees
Gyula Y. Katona, Péter G. N. Szabó
Let be a -uniform hypergraph. A chain in is a sequence of its vertices such that every consecutive vertices form an edge. In 1999 Katona and Kier…
Bounds on the Rubbling and Optimal Rubbling Numbers of Graphs
Gyula Y. Katona, Nandor Sieben
A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this…