4 papers · 1 filter
On the signed chromatic number of some classes of graphs
Julien Bensmail, Sandip Das, Soumen Nandi +3
A signed graph is a graph along with a function . A closed walk of a signed graph is positive (resp., negative) if it has an even (resp., odd) num…
Further Evidence Towards the Multiplicative 1-2-3 Conjecture
Julien Bensmail, Hervé Hocquard, Dimitri Lajou +1
The product version of the 1-2-3 Conjecture, introduced by Skowronek-Kazi{ó}w in 2012, states that, a few obvious exceptions apart, all graphs can be 3-edge-labelled so that no two…
Pushable chromatic number of graphs with degree constraints
Julien Bensmail, Sandip Das, Soumen Nandi +4
Pushable homomorphisms and the pushable chromatic number of oriented graphs were introduced by Klostermeyer and MacGillivray in 2004. They notably observed that, for any orie…
Orienting edges to fight fire in graphs
Julien Bensmail, Nick Brettell
We investigate a new oriented variant of the Firefighter Problem. In the traditional Firefighter Problem, a fire breaks out at a given vertex of a graph, and at each time interval…