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  1. No Access

    Article

    On the Kernel and Related Problems in Interval Digraphs

    Given a digraph G, a set \(X\subseteq V(G)\) X ⊆ ...

    Mathew C. Francis, Pavol Hell, Dalu Jacob in Algorithmica (2023)

  2. No Access

    Chapter and Conference Paper

    Bounding Threshold Dimension: Realizing Graphic Boolean Functions as the AND of Majority Gates

    A graph G on n vertices is a threshold graph if there exist real numbers \(a_1,a_2, \ldots , a_n\) and b such that the zero-one solutions...

    Mathew C. Francis, Atrayee Majumder… in Graph-Theoretic Concepts in Computer Scie… (2022)

  3. No Access

    Article

    On the Stab Number of Rectangle Intersection Graphs

    We introduce the notion of stab number and exact stab number of rectangle intersection graphs, otherwise known as graphs of boxicity at most 2. A graph G is said to be a k-stabbable rectangle intersection graph, ...

    Dibyayan Chakraborty, Mathew C. Francis in Theory of Computing Systems (2020)

  4. No Access

    Chapter and Conference Paper

    The Lexicographic Method for the Threshold Cover Problem

    The lexicographic method is a technique that was introduced by Hell and Huang [Journal of Graph Theory, 20(3): 361–374, 1995] as a way to simplify the problems of recognizing and obtaining representations of com...

    Mathew C. Francis, Dalu Jacob in Algorithms and Discrete Applied Mathematics (2020)

  5. No Access

    Chapter and Conference Paper

    On Rectangle Intersection Graphs with Stab Number at Most Two

    Rectangle intersection graphs are the intersection graphs of axis-parallel rectangles in the plane. A graph G is said to be a k-stabbable rectangle intersection graph, or k-SRIG for short, if it has a rectangle i...

    Dibyayan Chakraborty, Sandip Das… in Algorithms and Discrete Applied Mathematics (2019)

  6. No Access

    Article

    The Maximum Clique Problem in Multiple Interval Graphs

    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 i...

    Mathew C. Francis, Daniel Gonçalves, Pascal Ochem in Algorithmica (2015)

  7. No Access

    Article

    Cubicity and Bandwidth

    A unit cube in \({\mathbb{R}^k}\) (or a k-cube in short) is defined as the Cartesian product R 1 × R ...

    L. Sunil Chandran, Mathew C. Francis, Naveen Sivadasan in Graphs and Combinatorics (2013)

  8. No Access

    Chapter and Conference Paper

    The Maximum Clique Problem in Multiple Interval Graphs (Extended Abstract)

    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 i...

    Mathew C. Francis, Daniel Gonçalves… in Graph-Theoretic Concepts in Computer Scien… (2012)

  9. No Access

    Article

    Chordal Bipartite Graphs with High Boxicity

    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 induce...

    L. Sunil Chandran, Mathew C. Francis, Rogers Mathew in Graphs and Combinatorics (2011)

  10. No Access

    Article

    Boxicity of Leaf Powers

    The boxicity of a graph G, denoted as boxi(G), is defined as the minimum integer t such that G is an intersection graph of axis-parallel t-dimensional boxes. A graph G is a k-leaf power if there exists a tree T s...

    L. Sunil Chandran, Mathew C. Francis, Rogers Mathew in Graphs and Combinatorics (2011)

  11. No Access

    Article

    Geometric Representation of Graphs in Low Dimension Using Axis Parallel Boxes

    An axis-parallel k-dimensional box is a Cartesian product R 1×R 2×⋅⋅⋅×R k where R ...

    L. Sunil Chandran, Mathew C. Francis, Naveen Sivadasan in Algorithmica (2010)

  12. No Access

    Article

    On the Cubicity of Interval Graphs

    A k-cube (or “a unit cube in k dimensions”) is defined as the Cartesian product \(R_1 \times \cdots \times R_k\) wher...

    L. Sunil Chandran, Mathew C. Francis, Naveen Sivadasan in Graphs and Combinatorics (2009)

  13. No Access

    Chapter

    On the Cubicity of AT-Free Graphs and Circular-Arc Graphs

    A unit cube in k dimensions (k-cube) is defined as the Cartesian product R 1×R 2× ⋯ ×R k where R i ...

    L. Sunil Chandran, Mathew C. Francis… in Graph Theory, Computational Intelligence a… (2009)