22 citations · 31 across the 7 of their papers we have counts for
5 papers · 1 filter
Bounds for the Competition-Independence game on trees
Jan Petr, Julien Portier
In this paper we prove that Sweller has a strategy so that the Sweller-Start Competition-Independence game lasts at least moves for every tree. Moreover, we show that t…
On the number of minimum dominating sets and total dominating sets in forests
Jan Petr, Julien Portier, Leo Versteegen
We show that the maximum number of minimum dominating sets of a forest with domination number is at most and construct for each a tree with domination number $…
A note on Cops and Robbers, independence number, domination number and diameter
Jan Petr, Julien Portier, Leo Versteegen
We study relations between diameter , domination number , independence number and cop number of a connected graph , showing (i.) $c(G) \leq α(G)-\lfloo…
The odd chromatic number of a planar graph is at most 8
Jan Petr, Julien Portier
Petruševski and Škrekovski \cite{odd9} recently introduced the notion of an odd colouring of a graph: a proper vertex colouring of a graph is said to be \emph{odd} if for each…
A new lower bound on the pebbling number of the grid
Jan Petr, Julien Portier, Szymon Stolarczyk
A pebbling move on a graph consists of removing pebbles from a vertex and adding pebble to one of the neighbouring vertices. A vertex is called reachable if we can put …