Abstract. The crossing number of the Cartesian product C3 × Cn of a 3-cycle and an n-cycle is shown to be n.

In this paper, we show that the projective plane crossing number of the graphs C3 × Cn is n - 1 for n ≤ 5 and 2 for n = 4. As far as we can tell from the ...

The potency of an edge is the number of such pairs in which it appears. Thus the number of crossings in a drawing is half the sum of the potencies of the edges.

The main result of the paper is that the crossing number of the Cartesian product K2;3×C3 is 9. Besides, an upper bound of 4n for the crossing number of K2;3× ...

... The crossing number of C3 × Cn, J. Combin. Theory Ser. B 24, (1978) 134-136. [22] M. Kle˘s˘c, R. B. Richter, I. Stobert, The crossing number of C5 ×Cn, J.

Any drawing of C,, X Cn has many 4-cycles. Principal 4-cycles are analogous to the. 3-cycles or n-cycles in C3 X Cn. To verify the (4, n)-conjecture, Beineke ...

Dec 20, 2011 · Abstract. The crossing number is a popular tool in graph drawing and visualization, but there is not really just one crossing number; ...

Theorem 5.1 If G is 2–crossing–critical, then either cr(G) = 2 or G = C3 × C3. Since cr(C3 ×C3) = 3, so not every 2–crossing–critical graph has crossing number ...

Dec 20, 2011 · Abstract. The crossing number is a popular tool in graph drawing and visualization, but there is not really just one crossing number; ...

The author [11] calculated the projective plane crossing numbers of C3 ×Cn to be 2 for n=4 and n−1 for n¿ 4. Recently, a great deal of important work has been ...