TY - JOUR
T1 - Unit disk graphs
AU - Clark, Brent N.
AU - Colbourn, Charles J.
AU - Johnson, David S.
N1 - Funding Information:
of Toronto for hospitality during the time this paper was written. The research of the second author is supported by NSERC Canada under grant A0579.
PY - 1991/1/1
Y1 - 1991/1/1
N2 - Unit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) and for some problems in computational geometry. We show that many standard graph theoretic problems remain NP-complete on unit disk graphs, including coloring, independent set, domination, independent domination, and connected domination; NP-completeness for the domination problem is shown to hold even for grid graphs, a subclass of unit disk graphs. In contrast, we give a polynomial time algorithm for finding cliques when the geometric representation (circles in the plane) is provided.
AB - Unit disk graphs are the intersection graphs of equal sized circles in the plane: they provide a graph-theoretic model for broadcast networks (cellular networks) and for some problems in computational geometry. We show that many standard graph theoretic problems remain NP-complete on unit disk graphs, including coloring, independent set, domination, independent domination, and connected domination; NP-completeness for the domination problem is shown to hold even for grid graphs, a subclass of unit disk graphs. In contrast, we give a polynomial time algorithm for finding cliques when the geometric representation (circles in the plane) is provided.
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U2 - 10.1016/S0167-5060(08)71047-1
DO - 10.1016/S0167-5060(08)71047-1
M3 - Article
AN - SCOPUS:77957080877
VL - 48
SP - 165
EP - 177
JO - Annals of Discrete Mathematics
JF - Annals of Discrete Mathematics
SN - 0167-5060
IS - C
ER -