On the crossing numbers of Km□Cn and Km,l□Pn
- 作者：Zheng Wenping ; Lin Xiaohui ; Yang Yuansheng ; Deng Chengrui
- 关键词：Crossing number ; Cartesian product ; Complete graph ; Complete bipartite graph
- 刊名：Discrete Applied Mathematics
- 出版年：2008
- 期刊代码：46_0166218x
- 类别：cp
- 出版时间：28 May 2008
- 卷：156
- 期：10
- 页码：1892-1907
- 文件大小：383 K
摘要
Ringeisen and Beineke have proved that JP6G-1&_mathId=mml25&_user=1067359&_cdi=5629&_rdoc=29&_acct=C000050221&_version=1&_userid=10&md5=0739da61bba3c3944fba139ffe12bdf7" title="Click to view the MathML source" alt="Click to view the MathML source">cr(C3□Cn)=n and cct=C000050221&_version=1&_userid=10&md5=875460e279a1fd76cf0d0f3e3fe90904" title="Click to view the MathML source" alt="Click to view the MathML source">cr(K4□Cn)=3n. Bokal has proved that cct=C000050221&_version=1&_userid=10&md5=d80d2c00cab8077b4c47e8d92a2c5552">
. In this paper we study the crossing numbers of cct=C000050221&_version=1&_userid=10&md5=b51f82b753b2449ceba3cced111696c4" title="Click to view the MathML source" alt="Click to view the MathML source">Km□Cn and cct=C000050221&_version=1&_userid=10&md5=a616f823dc6212616590af80077ad460" title="Click to view the MathML source" alt="Click to view the MathML source">Km,l□Pn, and show (i) cct=C000050221&_version=1&_userid=10&md5=a3bce6e81685ad121aa3f420982b144e" title="Click to view the MathML source" alt="Click to view the MathML source">cr(Km□Cn)
n·cr(Km+2) for cct=C000050221&_version=1&_userid=10&md5=6656f03751fc8abe0008edbdee3f66a9" title="Click to view the MathML source" alt="Click to view the MathML source">n3 and cct=C000050221&_version=1&_userid=10&md5=30a7526017e78bae8d54380cb0f518fa" title="Click to view the MathML source" alt="Click to view the MathML source">m5; (ii) cct=C000050221&_version=1&_userid=10&md5=c16072f1fe0bf9a4cb2ebc6944ff3ec1">
for cct=C000050221&_version=1&_userid=10&md5=5398288a9e3548c813575da53028c3fd" title="Click to view the MathML source" alt="Click to view the MathML source">m=5,6,7 and for cct=C000050221&_version=1&_userid=10&md5=112c3b0ee1ca4c774cd55b9d54e521fc" title="Click to view the MathML source" alt="Click to view the MathML source">m8 with even cct=C000050221&_version=1&_userid=10&md5=1dd636fcd5455f6bbb803282b1f788d4" title="Click to view the MathML source" alt="Click to view the MathML source">n4, and equality holds for cct=C000050221&_version=1&_userid=10&md5=af260221e936634af5d09113f9648d9b" title="Click to view the MathML source" alt="Click to view the MathML source">m=5,6,7 and for cct=C000050221&_version=1&_userid=10&md5=bab4aaf7859e493dfaa7a051bd7b36bd" title="Click to view the MathML source" alt="Click to view the MathML source">m=8,9,10 with even cct=C000050221&_version=1&_userid=10&md5=07800ac40b112be249d0efd001b538fc" title="Click to view the MathML source" alt="Click to view the MathML source">n4 and (iii) cct=C000050221&_version=1&_userid=10&md5=4e91997e4af557ef1227df9a66215bf8">
for cct=C000050221&_version=1&_userid=10&md5=f70e461e8ed400b6df7e4cda38e1f6ad" title="Click to view the MathML source" alt="Click to view the MathML source">min(m,l)2, and equality holds for cct=C000050221&_version=1&_userid=10&md5=843157509c2a6f4a6307cc29bc7834d7" title="Click to view the MathML source" alt="Click to view the MathML source">min(m,l)=2.
n·cr(Km+2) for cct=C000050221&_version=1&_userid=10&md5=6656f03751fc8abe0008edbdee3f66a9" title="Click to view the MathML source" alt="Click to view the MathML source">n3 and cct=C000050221&_version=1&_userid=10&md5=30a7526017e78bae8d54380cb0f518fa" title="Click to view the MathML source" alt="Click to view the MathML source">m5; (ii) cct=C000050221&_version=1&_userid=10&md5=c16072f1fe0bf9a4cb2ebc6944ff3ec1">8 with even cct=C000050221&_version=1&_userid=10&md5=1dd636fcd5455f6bbb803282b1f788d4" title="Click to view the MathML source" alt="Click to view the MathML source">n4, and equality holds for cct=C000050221&_version=1&_userid=10&md5=af260221e936634af5d09113f9648d9b" title="Click to view the MathML source" alt="Click to view the MathML source">m=5,6,7 and for cct=C000050221&_version=1&_userid=10&md5=bab4aaf7859e493dfaa7a051bd7b36bd" title="Click to view the MathML source" alt="Click to view the MathML source">m=8,9,10 with even cct=C000050221&_version=1&_userid=10&md5=07800ac40b112be249d0efd001b538fc" title="Click to view the MathML source" alt="Click to view the MathML source">n4 and (iii) cct=C000050221&_version=1&_userid=10&md5=4e91997e4af557ef1227df9a66215bf8">2, and equality holds for cct=C000050221&_version=1&_userid=10&md5=843157509c2a6f4a6307cc29bc7834d7" title="Click to view the MathML source" alt="Click to view the MathML source">min(m,l)=2.