# 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 cubes have a non-empty intersection if and only if their corresponding vertices are adjacent. Moreover, when two cubes have a non-empty intersection, they just touch(More)
• Mutation research
• 1981
The report reviews and evaluates the current literature (about 125 primary publications) on chemically induced specific locus mutations in the V79 Chinese hamster lung cell line. The V79 cell is convenient to use for mutagenesis studies since it has a rapid growth rate, high plating efficiency, and a stable karyotype. Mutation can be easily measured at(More)
• J. Comb. Theory, Ser. B
• 2008
An axis-parallel d–dimensional box is a Cartesian product R1 × R2 × · · · × Rd where Ri (for 1 ≤ i ≤ d) is a closed interval of the form [ai, bi] on the real line. For a graph G, its boxicity box(G) is the minimum dimension d, such that G is representable as the intersection graph of (axis–parallel) boxes in d–dimensional space. The concept of boxicity(More)
• Algorithmica
• 2008
An axis-parallel k-dimensional box is a Cartesian product R 1×R 2×⋅⋅⋅×R k where R i (for 1≤i≤k) is a closed interval of the form [a i ,b i ] on the real line. For a graph G, its boxicity box (G) is the minimum dimension k, such that G is representable as the intersection graph of (axis-parallel) boxes in k-dimensional space. The concept of boxicity finds(More)
• 1
• SIAM J. Discrete Math.
• 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 S ′ ⊆ S of size at most k satisfying some desired properties. If S ′ is required to contain all the elements of U then it corresponds to the classical Set Cover(More)
• Graphs and Combinatorics
• 2011
The boxicity of a graph G is defined as the minimum integer k such that G is an intersection graph of axis-parallel k-dimensional boxes. Chordal bipartite graphs are bipartite graphs that do not contain an induced cycle of length greater than 4. It was conjectured by Otachi, Okamoto and Yamazaki that chordal bipartite graphs have boxicity at most 2. We(More)
• 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 CLIQUE problem in several classes of multiple interval graphs. The MAXIMUM CLIQUE problem, or the problem of finding the size of the maximum clique, is known to be(More)
• ArXiv
• 2006
A unit cube in k dimensional space (or k-cube in short) is defined as the Cartesian product R1 × R2 × · · · × Rk where Ri(for 1 ≤ i ≤ k) is a closed interval of the form [ai, ai + 1] on the real line. A k-cube representation of a graph G is a mapping of the vertices of G to k-cubes such that two vertices in G are adjacent if and only if their corresponding(More)
• Discrete Applied Mathematics
• 2016
A piecewise linear simple curve in the plane made up of k+1 line segments, each of which is either horizontal or vertical, with consecutive segments being of different orientation is called a k-bend path. Given a graph G, a collection of k-bend paths in which each path corresponds to a vertex in G and two paths have a common point if and only if the(More)