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- Stefan Felsner, Mathew C. Francis
- Symposium on Computational Geometry
- 2011

We prove that every planar graph has a representation using axis-parallel cubes in three dimensions in such a way that there is a cube corresponding to each vertex of the planar graph and two cubesâ€¦ (More)

- L. Sunil Chandran, Mathew C. Francis, Naveen Sivadasan
- J. Comb. Theory, Ser. B
- 2008

An axis-parallel dâ€“dimensional box is a Cartesian product R1 Ã— R2 Ã— Â· Â· Â· Ã— Rd where Ri (for 1 â‰¤ i â‰¤ d) is a closed interval of the form [ai, bi] on the real line. For a graph G, its boxicity box(G)â€¦ (More)

- Mathew C. Francis, Daniel GonÃ§alves, Pascal Ochem
- Algorithmica
- 2012

Multiple interval graphs are variants of interval graphs where instead of a single interval, each vertex is assigned a set of intervals on the real line. We study the complexity of the MAXIMUM CLIQUEâ€¦ (More)

- Manu Basavaraju, Mathew C. Francis, M. S. Ramanujan, Saket Saurabh
- FSTTCS
- 2013

In a typical covering problem we are given a universe U of size n, a family S (S could be given implicitly) of sizem and an integer k and the objective is to check whether there exists a subfamily Sâ€¦ (More)

- L. Sunil Chandran, Mathew C. Francis, Santhosh Suresh
- Discrete Mathematics
- 2009

A k-dimensional box is the Cartesian product R1 Ã— R2 Ã— Â· Â· Â· Ã—Rk where each Ri is a closed interval on the real line. The boxicity of a graph G, denoted as box(G) is the minimum integer k such that Gâ€¦ (More)

- Mathew C. Francis, Pavol Hell, Juraj Stacho
- SIAM J. Discrete Math.
- 2014

- Manu Basavaraju, Mathew C. Francis
- Journal of Graph Theory
- 2015

A strong edge colouring of a graph is an assignment of colours to the edges of the graph such that for every colour, the set of edges that are given that colour form an induced matching in the graph.â€¦ (More)

- L. Sunil Chandran, Mathew C. Francis, Naveen Sivadasan
- ArXiv
- 2006

A unit cube in k dimensional space (or k-cube in short) is defined as the Cartesian product R1 Ã— R2 Ã— Â· Â· Â· Ã— Rk where Ri(for 1 â‰¤ i â‰¤ k) is a closed interval of the form [ai, ai + 1] on the realâ€¦ (More)

- L. Sunil Chandran, Mathew C. Francis, Rogers Mathew
- Graphs and Combinatorics
- 2011

The boxicity of a graph G, denoted as box(G) is defined as the minimum integer t such that G is an intersection graph of axisparallel t-dimensional boxes. A graph G is a k-leaf power if there existsâ€¦ (More)

- Mathew C. Francis, Daniel GonÃ§alves
- Electronic Notes in Discrete Mathematics
- 2017

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 of interior disjointâ€¦ (More)