# 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)
• 3
• 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)
• 2
• 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)
• 1
• 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)
• 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)
• 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)
• 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)