On the choice number of complete multipartite graphs with part size four

详细信息    查看全文

• 作者：H.A. Kierstead^a ; ^{kierstead@asu.edu" class="auth_mail" title="E-mail the corresponding author} ; Andrew Salmon^b ; ^{andrew.salmon@yale.edu" class="auth_mail" title="E-mail the corresponding author} ; Ran Wang^a ; ^{rwang31@asu.edu" class="auth_mail" title="E-mail the corresponding author}
• 刊名：European Journal of Combinatorics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：58
• 期：Complete
• 页码：1-16
• 全文大小：470 K

文摘

Let hmlsrc">he MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300191&_mathId=si23.gif&_user=111111111&_pii=S0195669816300191&_rdoc=1&_issn=01956698&md5=63079d26df456a3b2dc8d91317ab7f30">height="15" width="37" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0195669816300191-si23.gif">hContainer hidden">hCode">h altimg="si23.gif" overflow="scroll">hvariant="normal">ch(G)h> denote the choice number of a graph hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300191&_mathId=si24.gif&_user=111111111&_pii=S0195669816300191&_rdoc=1&_issn=01956698&md5=21ded4ee0c55508e891dd3b97ad9347a" title="Click to view the MathML source">GhContainer hidden">hCode">h altimg="si24.gif" overflow="scroll">Gh>, and let hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300191&_mathId=si25.gif&_user=111111111&_pii=S0195669816300191&_rdoc=1&_issn=01956698&md5=f7471d8d41d1f21cfeff6c0e4255d295" title="Click to view the MathML source">K_s∗khContainer hidden">hCode">h altimg="si25.gif" overflow="scroll">Ks∗kh> be the complete hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300191&_mathId=si26.gif&_user=111111111&_pii=S0195669816300191&_rdoc=1&_issn=01956698&md5=fa7f29b069f81632ad6eed7ee6589c46" title="Click to view the MathML source">khContainer hidden">hCode">h altimg="si26.gif" overflow="scroll">kh>-partite graph with hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300191&_mathId=si27.gif&_user=111111111&_pii=S0195669816300191&_rdoc=1&_issn=01956698&md5=1c423c3f1cde9ae6f19867fcd4b2d9fd" title="Click to view the MathML source">shContainer hidden">hCode">h altimg="si27.gif" overflow="scroll">sh> vertices in each part. Erdős, Rubin, and Taylor showed that hmlsrc">he MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300191&_mathId=si28.gif&_user=111111111&_pii=S0195669816300191&_rdoc=1&_issn=01956698&md5=0f2d06d8350aedbe71ad29e255187164">height="15" width="87" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0195669816300191-si28.gif">hContainer hidden">hCode">h altimg="si28.gif" overflow="scroll">hvariant="normal">ch(K2∗k)=kh>, and suggested the problem of determining the choice number of hmlsrc">hImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300191&_mathId=si25.gif&_user=111111111&_pii=S0195669816300191&_rdoc=1&_issn=01956698&md5=f7471d8d41d1f21cfeff6c0e4255d295" title="Click to view the MathML source">K_s∗khContainer hidden">hCode">h altimg="si25.gif" overflow="scroll">Ks∗kh>. The first author established hmlsrc">he MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300191&_mathId=si30.gif&_user=111111111&_pii=S0195669816300191&_rdoc=1&_issn=01956698&md5=f812241c8372afe3dd1e0c6c44662c73">height="23" width="122" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0195669816300191-si30.gif">hContainer hidden">hCode">h altimg="si30.gif" overflow="scroll">hvariant="normal">ch(K3∗k)=⌈4k−13⌉h>. Here we prove hmlsrc">he MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0195669816300191&_mathId=si31.gif&_user=111111111&_pii=S0195669816300191&_rdoc=1&_issn=01956698&md5=12116f7e76b2176d3f23acbfdd5fc07d">height="23" width="123" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0195669816300191-si31.gif">hContainer hidden">hCode">h altimg="si31.gif" overflow="scroll">hvariant="normal">ch(K4∗k)=⌈3k−12⌉h>.