7 citations · 18 across the 18 of their papers we have counts for
5 papers · 1 filter
A proof of the 3/4 conjecture for the total domination game
Julien Portier, Leo Versteegen
In this paper we describe a strategy for Dominator that finishes the total domination game in at most moves for every graph on vertices without any isolated vertices…
A proof of the 3/5-conjecture in the domination game
Leo Versteegen
The domination game is an optimization game played by two players, Dominator and Staller, who alternately select vertices in a graph . A vertex is said to be dominated if it has…
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…
Improved bounds for the dimension of divisibility
Victor Souza, Leo Versteegen
The dimension of a partially-ordered set is the smallest integer such that one can embed into a product of linear orders. We prove that the dimension of the divisib…