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Relevant bibliographies by topics / Boxicity (Graphs)

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Journal articles
Dissertations / Theses
Book chapters

Academic literature on the topic 'Boxicity (Graphs)'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 September 2023

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Journal articles on the topic "Boxicity (Graphs)"

1

Trotter, W. T., and Douglas B. West. "Poset boxicity of graphs." Discrete Mathematics 64, no. 1 (1987): 105–7. http://dx.doi.org/10.1016/0012-365x(87)90247-0.

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Chandran, L. Sunil, Rogers Mathew, and Naveen Sivadasan. "Boxicity of line graphs." Discrete Mathematics 311, no. 21 (2011): 2359–67. http://dx.doi.org/10.1016/j.disc.2011.06.005.

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Sunil Chandran, L., Mathew C. Francis, and Santhosh Suresh. "Boxicity of Halin graphs." Discrete Mathematics 309, no. 10 (2009): 3233–37. http://dx.doi.org/10.1016/j.disc.2008.09.037.

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Bhowmick, Diptendu, and L. Sunil Chandran. "Boxicity of Circular Arc Graphs." Graphs and Combinatorics 27, no. 6 (2010): 769–83. http://dx.doi.org/10.1007/s00373-010-1002-1.

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Esperet, Louis, and Gwenaël Joret. "Boxicity of Graphs on Surfaces." Graphs and Combinatorics 29, no. 3 (2012): 417–27. http://dx.doi.org/10.1007/s00373-012-1130-x.

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Bellantoni, S., I. Ben-Arroyo Hartman, T. Przytycka, and S. Whitesides. "Grid intersection graphs and boxicity." Discrete Mathematics 114, no. 1-3 (1993): 41–49. http://dx.doi.org/10.1016/0012-365x(93)90354-v.

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Bohra, Ankur, L. Sunil Chandran, and J. Krishnam Raju. "Boxicity of series-parallel graphs." Discrete Mathematics 306, no. 18 (2006): 2219–21. http://dx.doi.org/10.1016/j.disc.2006.04.014.

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Chandran, L. Sunil, Mathew C. Francis, and Rogers Mathew. "Chordal Bipartite Graphs with High Boxicity." Graphs and Combinatorics 27, no. 3 (2011): 353–62. http://dx.doi.org/10.1007/s00373-011-1017-2.

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Esperet, Louis. "Boxicity of graphs with bounded degree." European Journal of Combinatorics 30, no. 5 (2009): 1277–80. http://dx.doi.org/10.1016/j.ejc.2008.10.003.

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Chandran, L. Sunil, Wilfried Imrich, Rogers Mathew, and Deepak Rajendraprasad. "Boxicity and cubicity of product graphs." European Journal of Combinatorics 48 (August 2015): 100–109. http://dx.doi.org/10.1016/j.ejc.2015.02.013.

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Dissertations / Theses on the topic "Boxicity (Graphs)"

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Shah, Chintan D. "Boxicity, Cubicity And Vertex Cover." Thesis, 2008. https://etd.iisc.ac.in/handle/2005/890.

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The boxicity of a graph G, denoted as box(G), is the minimum dimension d for which each vertex of G can be mapped to a d-dimensional axis-parallel box in Rd such that two boxes intersect if and only if the corresponding vertices of G are adjacent. An axis-parallel box is a generalized rectangle with sides parallel to the coordinate axes. If additionally, we restrict all sides of the rectangle to be of unit length, the new parameter so obtained is called the cubicity of the graph G, denoted by cub(G). F.S. Roberts had shown that for a graph G with n vertices, box(G) ≤ and cub(G) ≤ . A mi

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Shah, Chintan D. "Boxicity, Cubicity And Vertex Cover." Thesis, 2008. http://hdl.handle.net/2005/890.

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The boxicity of a graph G, denoted as box(G), is the minimum dimension d for which each vertex of G can be mapped to a d-dimensional axis-parallel box in Rd such that two boxes intersect if and only if the corresponding vertices of G are adjacent. An axis-parallel box is a generalized rectangle with sides parallel to the coordinate axes. If additionally, we restrict all sides of the rectangle to be of unit length, the new parameter so obtained is called the cubicity of the graph G, denoted by cub(G). F.S. Roberts had shown that for a graph G with n vertices, box(G) ≤ and cub(G) ≤ . A min

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Mathew, Rogers. "Boxicity And Cubicity : A Study On Special Classes Of Graphs." Thesis, 2012. https://etd.iisc.ac.in/handle/2005/2320.

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Let F be a family of sets. A graph G is an intersection graph of sets from the family F if there exists a mapping f : V (G)→ F such that, An interval graph is an intersection graph of a family of closed intervals on the real line. Interval graphs find application in diverse fields ranging from DNA analysis to VLSI design. An interval on the real line can be generalized to a k dimensional box or k-box. A k-box B = (R1.R2….Rk) is defined to be the Cartesian product R1 × R2 × …× Rk, where each Ri is a closed interval on the real line. If each Ri is a unit length interval, we call B a k-cube. T

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Mathew, Rogers. "Boxicity And Cubicity : A Study On Special Classes Of Graphs." Thesis, 2012. http://etd.iisc.ernet.in/handle/2005/2320.

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Let F be a family of sets. A graph G is an intersection graph of sets from the family F if there exists a mapping f : V (G)→ F such that, An interval graph is an intersection graph of a family of closed intervals on the real line. Interval graphs find application in diverse fields ranging from DNA analysis to VLSI design. An interval on the real line can be generalized to a k dimensional box or k-box. A k-box B = (R1.R2….Rk) is defined to be the Cartesian product R1 × R2 × …× Rk, where each Ri is a closed interval on the real line. If each Ri is a unit length interval, we call B a k-cube. Th

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Francis, Mathew C. "Intersection Graphs Of Boxes And Cubes." Thesis, 2009. https://etd.iisc.ac.in/handle/2005/1027.

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A graph Gis said to be an intersection graph of sets from a family of sets if there exists a function ƒ : V(G)→ such that for u,v V(G), (u,v) E(G) ƒ (u) ƒ (v) ≠ . Interval graphs are thus the intersection graphs of closed intervals on the real line and unit interval graphs are the intersection graphs of unit length intervals on the real line. An interval on the real line can be generalized to a “kbox” in Rk.A kbox B =(R1,R2,...,Rk), where each Riis a closed interval on the real line, is defined to be the Cartesian product R1x R2x…x Rk. If each Ri is a unit length interval, we call B

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Francis, Mathew C. "Intersection Graphs Of Boxes And Cubes." Thesis, 2009. http://hdl.handle.net/2005/1027.

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A graph Gis said to be an intersection graph of sets from a family of sets if there exists a function ƒ : V(G)→ such that for u,v V(G), (u,v) E(G) ƒ (u) ƒ (v) ≠ . Interval graphs are thus the intersection graphs of closed intervals on the real line and unit interval graphs are the intersection graphs of unit length intervals on the real line. An interval on the real line can be generalized to a “kbox” in Rk.A kbox B =(R1,R2,...,Rk), where each Riis a closed interval on the real line, is defined to be the Cartesian product R1x R2x…x Rk. If each Ri is a unit length interval, we call B

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Rajendraprasad, Deepak. "Rainbow Colouring and Some Dimensional Problems in Graph Theory." Thesis, 2013. https://etd.iisc.ac.in/handle/2005/3336.

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This thesis touches three diﬀerent topics in graph theory, namely, rainbow colouring, product dimension and boxicity. Rainbow colouring An edge colouring of a graph is called a rainbow colouring, if every pair of vertices is connected by atleast one path in which no two edges are coloured the same. The rainbow connection number of a graph is the minimum number of colours required to rainbow colour it. In this thesis we give upper bounds on rainbow connection number based on graph invariants like minimum degree, vertex connectivity, and radius. We also give some computational complexity result

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Rajendraprasad, Deepak. "Rainbow Colouring and Some Dimensional Problems in Graph Theory." Thesis, 2013. http://etd.iisc.ernet.in/2005/3336.

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This thesis touches three diﬀerent topics in graph theory, namely, rainbow colouring, product dimension and boxicity. Rainbow colouring An edge colouring of a graph is called a rainbow colouring, if every pair of vertices is connected by atleast one path in which no two edges are coloured the same. The rainbow connection number of a graph is the minimum number of colours required to rainbow colour it. In this thesis we give upper bounds on rainbow connection number based on graph invariants like minimum degree, vertex connectivity, and radius. We also give some computational complexity results

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Adiga, Abhijin. "On Dimensional Parameters Of Graphs And Posets." Thesis, 2011. https://etd.iisc.ac.in/handle/2005/2071.

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In this thesis we study the following dimensional parameters : boxicity, cubicity, threshold dimension and poset dimension. While the ﬁrst three parameters are defined on graphs, poset dimension is defined on partially ordered sets (or posets). We only consider finite graphs and posets. In addition, we assume that the graphs are simple and undirected. Boxicity and Cubicity: A k-box (k-cube) is a Cartesian product of closed intervals(unit-intervals) [a1,b1]x…x [ak,bk]. The boxicity (cubicity) of a graph G,box (G) (cub(G)) is the minimum integer k such that every vertex in G is mapped to a k-b

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Adiga, Abhijin. "On Dimensional Parameters Of Graphs And Posets." Thesis, 2011. http://etd.iisc.ernet.in/handle/2005/2071.

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Abstract:

In this thesis we study the following dimensional parameters : boxicity, cubicity, threshold dimension and poset dimension. While the ﬁrst three parameters are defined on graphs, poset dimension is defined on partially ordered sets (or posets). We only consider finite graphs and posets. In addition, we assume that the graphs are simple and undirected. Boxicity and Cubicity: A k-box (k-cube) is a Cartesian product of closed intervals(unit-intervals) [a1,b1]x…x [ak,bk]. The boxicity (cubicity) of a graph G,box (G) (cub(G)) is the minimum integer k such that every vertex in G is mapped to a k-bo

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Book chapters on the topic "Boxicity (Graphs)"

1

Chandran, L. Sunil, Wilfried Imrich, Rogers Mathew, and Deepak Rajendraprasad. "Boxicity and cubicity of product graphs." In The Seventh European Conference on Combinatorics, Graph Theory and Applications. Scuola Normale Superiore, 2013. http://dx.doi.org/10.1007/978-88-7642-475-5_38.

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Bhore, Sujoy Kumar, Dibyayan Chakraborty, Sandip Das, and Sagnik Sen. "On a Special Class of Boxicity 2 Graphs." In Algorithms and Discrete Applied Mathematics. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-14974-5_16.

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Adiga, Abhijin, Jasine Babu, and L. Sunil Chandran. "A Constant Factor Approximation Algorithm for Boxicity of Circular Arc Graphs." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-22300-6_2.

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Bruhn, Henning, Morgan Chopin, Felix Joos, and Oliver Schaudt. "Structural Parameterizations for Boxicity." In Graph-Theoretic Concepts in Computer Science. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12340-0_10.

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5

Basavaraju, Manu, L. Sunil Chandran, Martin Charles Golumbic, Rogers Mathew, and Deepak Rajendraprasad. "Boxicity and Separation Dimension." In Graph-Theoretic Concepts in Computer Science. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-12340-0_7.

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