IJPAM: Volume 13, No. 4 (2004)

DISCRETE REALIZATIONS OF CONTACT
AND INTERSECTION GRAPHS

Jurek Czyzowicz$^1$, Evangelos Kranakis$^2$,
Danny Krizanc$^3$, Jorge Urrutia$^4$
$^1$Département d'Informatique
Université du Québec à Hull
Hull, Québec J8X 3X7, CANADA
e-mail: czyzowicz@uqah.uquebec.ca
$^{2,3}$School of Computer Science
Carleton University
Ottawa, ON, K1S 5B6, CANADA
$^2$e-mail: kranakis@scs.carleton.ca
$^3$e-mail: krizanc@scs.carleton.ca
$^4$Department of Computer Science
University of Ottawa
Ottawa, ON, K1N 9B4, CANADA
e-mail: jorge@site.uottawa.ca


Abstract.Known realizations of geometric representations of graphs, like contact, intersection, etc., are ``continuous'', in the sense that the geometric objects are drawn in Euclidean space with real numbers as coordinates. In this paper, we initiate the study of dicrete versions of contact and intersection graphs and examine their relation to their continuous counterparts. The classes of graphs arising appear to have interesting properties and are thus interesting in their own right. We also study realizability, characterizations as well as intractability questions for the resulting new classes of graphs.

Received: February 1, 2004

AMS Subject Classification: 68R10, 68U05

Key Words and Phrases: coin, contact, intersection, interval graphs, discrete, planar graphs, $\np$

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 13
Issue: 4