21 citations · 34 across the 21 of their papers we have counts for
27 papers
A -centered coloring for the grid using colors
Mathew Francis, Drimit Pattanayak
A -centered coloring of a graph , where is a positive integer, is a coloring of the vertices of in such a way that every connected subgraph of either contains a v…
Bounding threshold dimension: realizing graphic Boolean functions as the AND of majority gates
Mathew C. Francis, Atrayee Majumder, Rogers Mathew
A graph on vertices is a \emph{threshold graph} if there exist real numbers and such that the zero-one solutions of the linear inequality $\sum \…
Variants of the Gyàrfàs-Sumner Conjecture: Oriented Trees and Rainbow Paths
Manu Basavaraju, L. Sunil Chandran, Mathew C. Francis +1
Given a finite family of graphs, we say that a graph is "-free" if does not contain any graph in as a subgraph. A vertex-colored gr…
Weakening Total Coloring Conjecture: Weak TCC and Hadwiger's Conjecture on Total Graphs
Manu Basavaraju, L. Sunil Chandran, Mathew C. Francis +1
Hadwiger's conjecture is one of the most important and long-standing conjectures in graph theory. Reed and Seymour showed in 2004 that Hadwiger's conjecture is true for line graphs…
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…
Recognizing -Clique Extendible Orderings
Mathew Francis, Rian Neogi, Venkatesh Raman
A graph is -clique-extendible if there is an ordering of the vertices such that whenever two -sized overlapping cliques and have common vertices, and these comm…