On local structures of cubicity 2 graphs

Authors

Sujoy Bhore, Ben-Gurion University of the Negev
Dibyayan Chakraborty, Indian Statistical Institute, Kolkata
Sandip Das, Indian Statistical Institute, Kolkata
Sagnik Sen, Indian Statistical Institute Bangalore

Document Type

Conference Article

Publication Title

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

Abstract

A 2-stab unit interval graph (2SUIG) is an axes-parallel unit square intersection graph where the unit squares intersect either of the two fixed lines parallel to the X-axis, distance 1 + ε (0 < ε < 1) apart. This family of graphs allow us to study local structures of unit square intersection graphs, that is, graphs with cubicity 2. The complexity of determining whether a tree has cubicity 2 is unknown while the graph recognition problem for unit square intersection graph is known to be NP-hard. We present a linear time algorithm for recognizing trees that admit a 2SUIG representation.

First Page

254

Last Page

269

DOI

10.1007/978-3-319-48749-6_19

Publication Date

1-1-2016

Comments

Open Access; Green Open Access

Recommended Citation

Bhore, Sujoy; Chakraborty, Dibyayan; Das, Sandip; and Sen, Sagnik, "On local structures of cubicity 2 graphs" (2016). Conference Articles. 764.
https://digitalcommons.isical.ac.in/conf-articles/764