21 citations · 34 across the 21 of their papers we have counts for
4 papers · 2 filters
On Graphs whose Eternal Vertex Cover Number and Vertex Cover Number Coincide
Jasine Babu, L. Sunil Chandran, Mathew Francis +3
The eternal vertex cover problem is a variant of the classical vertex cover problem where a set of guards on the vertices have to be dynamically reconfigured from one vertex cover…
Dushnik-Miller dimension of d-dimensional tilings with boxes
Mathew C. Francis, Daniel Gonçalves
Planar graphs are the graphs with Dushnik-Miller dimension at most three (W. Schnyder, Planar graphs and poset dimension, Order 5, 323-343, 1989). Consider the intersection graph o…
Extending some results on the second neighborhood conjecture
Suresh Dara, Mathew C. Francis, Dalu Jacob +1
A vertex in a directed graph is said to have a large second neighborhood if it has at least as many second out-neighbors as out-neighbors. The Second Neighborhood Conjecture, first…
On the stab number of rectangle intersection graphs
Dibyayan Chakraborty, Mathew C. Francis
We introduce the notion of \emph{stab number} and \emph{exact stab number} of rectangle intersection graphs, otherwise known as graphs of boxicity at most 2. A graph is said to…