Lower bounds for the game colouring number of partial k-trees and planar graphs

详细信息	查看全文 | 推荐本文 |

• 作者：Jiaojiao Wu ; Xuding Zhu
• 关键词：Game colouring number ; Game chromatic number ; Partial 23">none ; color ; black" href="/science?_ob=MathURL&_method=retrieve&_udi=B6V00-4NXHCDS-1&_mathId=mml23&_user=1067359&_cdi=5632&_rdoc=36&_acct=C000050221&_versio
• 刊名：Discrete Mathematics
• 出版年：2008
• 期刊代码：47_0012365x
• 类别：cp
• 出版时间：28 June 2008
• 卷：308
• 期：12
• 页码：2637-2642
• 文件大小：147 K

摘要

This paper discusses the game colouring number of partial k-trees and planar graphs. Let 2&_rdoc=36&_acct=C000050221&_version=1&_userid=10&md5=6e783d960feb47de70390931fe5a5398">24/0?wchp=dGLbVtb-zSkWz" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=18 width="78"/> and 2&_rdoc=36&_acct=C000050221&_version=1&_userid=10&md5=9b5c138cd1ebe0257e21015d99b1ed3d">2H/0?wchp=dGLbVtb-zSkWz" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=18 width="54"/> denote the maximum game colouring number of partial k trees and the maximum game colouring number of planar graphs, respectively. In this paper, we prove that 2&_rdoc=36&_acct=C000050221&_version=1&_userid=10&md5=8a554498db609d06a06b70a62a716f42">2X/0?wchp=dGLbVtb-zSkWz" alt="View the MathML source" title="View the MathML source" align="absbottom" border="0" height=18 width="150"/> and 2&_rdoc=36&_acct=C000050221&_version=1&_userid=10&md5=df83351b1412acb32bfb6cefe561717d">. We also prove that the game colouring number 2&_rdoc=36&_acct=C000050221&_version=1&_userid=10&md5=5217fea615a6fb26e22b6dd51f0a68c3" title="Click to view the MathML source" alt="Click to view the MathML source">col_g(G) of a graph is a monotone parameter, i.e., if 20">20&_user=1067359&_cdi=5632&_rdoc=36&_acct=C000050221&_version=1&_userid=10&md5=a6d85bde26d535f73ddcf78408bbb8c5" title="Click to view the MathML source" alt="Click to view the MathML source">H is a subgraph of 21">21&_user=1067359&_cdi=5632&_rdoc=36&_acct=C000050221&_version=1&_userid=10&md5=7ac3df15f3a27445915b985aa42dbf86" title="Click to view the MathML source" alt="Click to view the MathML source">G, then 22">22&_user=1067359&_cdi=5632&_rdoc=36&_acct=C000050221&_version=1&_userid=10&md5=57b57920519b063393cf265dad5d0aa2" title="Click to view the MathML source" alt="Click to view the MathML source">col_g(H)2a7d.gif" alt="less-than-or-equals, slant" title="less-than-or-equals, slant" border="0">col_g(G).