Lemma 1.2 shows that if D is a drawing of K 13 with 217 crossings, then there are vertices u and v such that D − u is a drawing of K 12 with the property that δ ...

Jul 12, 2013 · If there is one, then cr(K13) < 225, while if there is not, then cr(K13) > 217. Equation 1.1 shows that, if D is a drawing of K12 having 151 ...

Since the crossing number of K 12 is now known to be 150, it is well-known that simple counting arguments and Kleitman's parity theorem for the crossing ...

The crossing number of K 13 is known to be between 219 [12] and 225 [18]. For odd n, the crossing number has the same parity as H(n) [13]. ... All Good ...

heavily computer assisted proof that the crossing number of the complete graph K13 is cr(13) = 225. This implies that cr(14) = 315. Original language, English.

The smallest unsolved case is K13 with conjectured crossing number 225. For many graph classes the situation is similar: cr(G) is known for small instances ...

Hence, there are only two possibilities remaining for the crossing number of K13; either 223 or 225. ... The proof files for the crossing numbers determined by ...

On the crossing number of K13 · Drawings of complete graphs in the projective plane · A new infinite family of 4-regular crossing-critical graphs · Convex drawings ...

The crossing number of K13 is known to be between 219 [12] and 225 [18]. For odd n, the crossing number has the same parity as H(n) [13]. For a drawing D of Kn ...

For example, to the time of this writing, the crossing number of K13 remains unknown. Perhaps even more surprisingly, the Minimum Crossing Number problem ...