21 citations · 34 across the 21 of their papers we have counts for
13 papers · 1 filter
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…
The linear arboricity conjecture for graphs of low degeneracy
Manu Basavaraju, Arijit Bishnu, Mathew Francis +1
A linear forest is an acyclic graph whose each connected component is a path; or in other words, it is an acyclic graph whose maximum degree is at most 2. A linear coloring of a gr…
On Induced Colourful Paths in Triangle-free Graphs
Jasine Babu, Manu Basavaraju, L. Sunil Chandran +1
Given a graph whose vertices have been properly coloured, we say that a path in is "colourful" if no two vertices in the path have the same colour. It is a corollary…