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Algorithms 2013, 6(1), 60-83; doi:10.3390/a6010060
Article

Tractabilities and Intractabilities on Geometric Intersection Graphs

School of Information Science, Japan Advanced Institute of Science and Technology, Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
Parts of Results were Presented at ISAAC 2008 and WALCOM 2008.
Received: 23 October 2012 / Revised: 10 January 2013 / Accepted: 14 January 2013 / Published: 25 January 2013
(This article belongs to the Special Issue Graph Algorithms)
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Abstract

A graph is said to be an intersection graph if there is a set of objects such that each vertex corresponds to an object and two vertices are adjacent if and only if the corresponding objects have a nonempty intersection. There are several natural graph classes that have geometric intersection representations. The geometric representations sometimes help to prove tractability/intractability of problems on graph classes. In this paper, we show some results proved by using geometric representations.
Keywords: bandwidth; chain graphs; graph isomorphism; Hamiltonian path problem; interval graphs; threshold graphs; unit grid intersection graphs bandwidth; chain graphs; graph isomorphism; Hamiltonian path problem; interval graphs; threshold graphs; unit grid intersection graphs
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Uehara, R. Tractabilities and Intractabilities on Geometric Intersection Graphs. Algorithms 2013, 6, 60-83.

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