TY - GEN

T1 - On a special class of boxicity 2 graphs

AU - Bhore, Sujoy Kumar

AU - Chakraborty, Dibyayan

AU - Das, Sandip

AU - Sen, Sagnik

N1 - Publisher Copyright:
© 2015, Springer International Publishing Switzerland.

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We define and study a class of graphs, called 2-stab interval graphs (2SIG), with boxicity 2 which properly contains the class of interval graphs. A 2SIG is an axes-parallel rectangle intersection graph where the rectangles have unit height (that is, length of the side parallel to Y - axis) and intersects either of the two fixed lines, parallel to the X-axis, distance 1 + ε (0 < ε < 1) apart. Intuitively, 2SIG is a graph obtained by putting some edges between two interval graphs in a particular rule. It turns out that for these kind of graphs, the chromatic number of any of its induced subgraphs is bounded by twice of its (induced subgraph) clique number. This shows that the graph, even though not perfect, is not very far from it. Then we prove similar results for some subclasses of 2SIG and provide efficient algorithm for finding their clique number. We provide a matrix characterization for a subclass of 2SIG graph.

AB - We define and study a class of graphs, called 2-stab interval graphs (2SIG), with boxicity 2 which properly contains the class of interval graphs. A 2SIG is an axes-parallel rectangle intersection graph where the rectangles have unit height (that is, length of the side parallel to Y - axis) and intersects either of the two fixed lines, parallel to the X-axis, distance 1 + ε (0 < ε < 1) apart. Intuitively, 2SIG is a graph obtained by putting some edges between two interval graphs in a particular rule. It turns out that for these kind of graphs, the chromatic number of any of its induced subgraphs is bounded by twice of its (induced subgraph) clique number. This shows that the graph, even though not perfect, is not very far from it. Then we prove similar results for some subclasses of 2SIG and provide efficient algorithm for finding their clique number. We provide a matrix characterization for a subclass of 2SIG graph.

UR - http://www.scopus.com/inward/record.url?scp=84922287330&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-14974-5_16

DO - 10.1007/978-3-319-14974-5_16

M3 - Conference contribution

AN - SCOPUS:84922287330

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 157

EP - 168

BT - Algorithms and Discrete Applied Mathematics - 1st International Conference, CALDAM 2015, Proceedings

A2 - Ganguly, Sumit

A2 - Krishnamurti, Ramesh

PB - Springer Verlag

T2 - 1st International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2015

Y2 - 8 February 2015 through 10 February 2015

ER -