5 papers · 1 filter
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…
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…
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…