Some provably hard crossing number problems
نویسندگان
چکیده
منابع مشابه
Crossing Number is Hard for Kernelization
The graph crossing number problem, cr(G) ≤ k, asks for a drawing of a graph G in the plane with at most k edge crossings. Although this problem is in general notoriously difficult, it is fixedparameter tractable for the parameter k [Grohe]. This suggests a closely related question of whether this problem has a polynomial kernel, meaning whether every instance of cr(G) ≤ k can be in polynomial t...
متن کاملCrossing Number Is Hard for Cubic Graphs
It was proved by [Garey and Johnson, 1983] that computing the crossing number of a graph is an NP -hard problem. Their reduction, however, used parallel edges and vertices of very high degrees. We prove here that it is NP -hard to determine the crossing number of a simple cubic graph. In particular, this implies that the minor-monotone version of crossing number is also NP -hard, which has been...
متن کاملCrossing Number is Hard for Kernelization
The graph crossing number problem, cr(G) ≤ k, asks for a drawing of a graph G in the plane with at most k edge crossings. Although this problem is in general notoriously difficult, it is fixedparameter tractable for the parameter k [Grohe]. This suggests a closely related question of whether this problem has a polynomial kernel, meaning whether every instance of cr(G) ≤ k can be in polynomial t...
متن کاملCrossing Numbers and Hard Erdös Problems in Discrete Geometry
We show that an old but not well-known lower bound for the crossing number of a graph yields short proofs for a number of bounds in discrete plane geometry which were considered hard before: the number of incidences among points and lines, the maximum number of unit distances among n points, the minimum number of distinct distances among n points. " A statement about curves is not interesting u...
متن کاملOdd Crossing Number Is Not Crossing Number
The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the number of pairs of edges that intersect an odd number of times, we obtain the odd crossing number. We show that there is a graph for which these two concepts differ, answering a well-known open question on crossing numbe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete & Computational Geometry
سال: 1991
ISSN: 0179-5376,1432-0444
DOI: 10.1007/bf02574701