TY - JOUR

T1 - Unit disk graphs

AU - Clark, Brent N.

AU - Colbourn, Charles J.

AU - Johnson, David S.

N1 - Funding Information:
of Toronto for hospitalityd uring the time this paper was written. The researcho f the seconda uthor is supportedb y NSERC Canadau nder grant A0579.

PY - 1990/12/14

Y1 - 1990/12/14

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 - 10.1016/0012-365X(90)90358-O

DO - 10.1016/0012-365X(90)90358-O

M3 - Article

AN - SCOPUS:0000839639

SN - 0012-365X

VL - 86

SP - 165

EP - 177

JO - Discrete Mathematics

JF - Discrete Mathematics

IS - 1-3

ER -