منابع مشابه
Crossing Number of Toroidal Graphs
It is shown that if a graph of n vertices can be drawn on the torus without edge crossings and the maximum degree of its vertices is at most d, then its planar crossing number cannot exceed cdn, where c is a constant. This bound, conjectured by Brass, cannot be improved, apart from the value of the constant. We strengthen and generalize this result to the case when the graph has a crossing-free...
متن کاملThe toroidal crossing number of K4, n
In this paper, we study the crossing number of the complete bipartite graph K4,n in torus and obtain crT (K4,n) = ⌊ n 4 ⌋(2n− 4(1 + ⌊ n 4 ⌋)).
متن کاملApproximating the Crossing Number of Toroidal Graphs
CrossingNumber is one of the most challenging algorithmic problems in topological graph theory, with applications to graph drawing and VLSI layout. No polynomial time approximation algorithm is known for this NP-Complete problem. We give in this paper a polynomial time approximation algorithm for the crossing number of toroidal graphs with bounded degree. In course of proving the algorithm we p...
متن کاملAnalogies between the crossing number and the tangle crossing number
Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two leaf-sets. These objects are of use in phylogenetics and are represented with straightline drawings where the leaves of the two plane binary trees are on two parallel lines and only the matching edges can cross. The tangle crossing number of a tangl...
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...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory
سال: 1969
ISSN: 0021-9800
DOI: 10.1016/s0021-9800(69)80084-0