21 citations · 34 across the 21 of their papers we have counts for
13 papers · 1 filter
On the Kernel and Related Problems in Interval Digraphs
Mathew C. Francis, Pavol Hell, Dalu Jacob
Given a digraph , a set is said to be absorbing set (resp. dominating set) if every vertex in the graph is either in or is an in-neighbour (resp. out-neigh…
Representing graphs as the intersection of cographs and threshold graphs
Daphna Chacko, Mathew C. Francis
A graph is said to be the intersection of graphs if and . For a graph ,…
The Lexicographic Method for the Threshold Cover Problem
Mathew C. Francis, Dalu Jacob
Threshold graphs are a class of graphs that have many equivalent definitions and have applications in integer programming and set packing problems. A graph is said to have a thresh…
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…