Rainbow copies of in edge-colored hypercubes

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• 作者：Jó ; zsef Balogh^a ; ^b ; ^{jobal@math.uiuc.edu" class="auth_mail" title="E-mail the corresponding author} ; Michelle Delcourt^c ; ^{delcour2@illinois.edu" class="auth_mail" title="E-mail the corresponding author} ; Bernard Lidický ; ^d ; ¹ ; ^{lidicky@iastate.edu" class="auth_mail" title="E-mail the corresponding author} ; Cory Palmer^e ; ² ; ^{cory.palmer@umontana.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Edge-coloring ; Hypercube ; Rainbow
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：10 September 2016
• 年：2016
• 卷：210
• 期：Complete
• 页码：35-37
• 全文大小：346 K

文摘

For positive integers 92c" title="Click to view the MathML source">k$k$ and d$d$ such that 4≤k<d$4\le k<d$ and k≠5$k\ne 5$, we determine the maximum number of rainbow colored copies of c0533790e783985" title="Click to view the MathML source">C₄$C_4$ in a 92c" title="Click to view the MathML source">k$k$-edge-coloring of the d$d$-dimensional hypercube Q_d${\mathcal{Q}}_d$. Interestingly, the 92c" title="Click to view the MathML source">k$k$-edge-colorings of Q_d${\mathcal{Q}}_d$ yielding the maximum number of rainbow copies of c0533790e783985" title="Click to view the MathML source">C₄$C_4$ also have the property that every copy of c0533790e783985" title="Click to view the MathML source">C₄$C_4$ which is not rainbow is monochromatic.