TY - JOUR

T1 - Intersection graphs of curves in the plane

AU - Ehrlich, G.

AU - Even, S.

AU - Tarjan, R. E.

PY - 1976/8

Y1 - 1976/8

N2 - Let V be a set of curves in the plane. The corresponding intersection graph has V as the set of vertices, and two vertices are connected by an edge if and only if the two corresponding curves intersect in the plane. It is shown that the set of intersection graphs of curves in the plane is a proper subset of the set of all undirected graphs. Furthermore, the set of intersection graphs of straight line-segments is a proper subset of the set of the intersection graphs of curves in the plane. Finally, it is shown that for every k ≥ 3, the problem of determining whether an intersection graph of straight line-segments is k-colorable is NP-complete.

AB - Let V be a set of curves in the plane. The corresponding intersection graph has V as the set of vertices, and two vertices are connected by an edge if and only if the two corresponding curves intersect in the plane. It is shown that the set of intersection graphs of curves in the plane is a proper subset of the set of all undirected graphs. Furthermore, the set of intersection graphs of straight line-segments is a proper subset of the set of the intersection graphs of curves in the plane. Finally, it is shown that for every k ≥ 3, the problem of determining whether an intersection graph of straight line-segments is k-colorable is NP-complete.

UR - http://www.scopus.com/inward/record.url?scp=0001769885&partnerID=8YFLogxK

U2 - 10.1016/0095-8956(76)90022-8

DO - 10.1016/0095-8956(76)90022-8

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AN - SCOPUS:0001769885

SN - 0095-8956

VL - 21

SP - 8

EP - 20

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

IS - 1

ER -