On a special class of boxicity 2 graphs

Sujoy Kumar Bhore, Dibyayan Chakraborty, Sandip Das, Sagnik Sen

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

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.

Original languageEnglish
Title of host publicationAlgorithms and Discrete Applied Mathematics - 1st International Conference, CALDAM 2015, Proceedings
EditorsSumit Ganguly, Ramesh Krishnamurti
PublisherSpringer Verlag
Pages157-168
Number of pages12
ISBN (Electronic)9783319149738
DOIs
StatePublished - 1 Jan 2015
Externally publishedYes
Event1st International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2015 - Kanpur, India
Duration: 8 Feb 201510 Feb 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume8959
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference1st International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2015
Country/TerritoryIndia
CityKanpur
Period8/02/1510/02/15

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)

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