On the existence of unparalleled even cycle systems

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• 作者：Peter Danziger ^{danziger@ryerson.ca" class="auth_mail" title="E-mail the corresponding author} ; Eric Mendelsohn ^{mendelso@math.utoronto.ca" class="auth_mail" title="E-mail the corresponding author} ; Tommaso Traetta ^{tommaso.traetta@ryerson.ca" class="auth_mail" title="E-mail the corresponding author traetta.tommaso@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 刊名：European Journal of Combinatorics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：59
• 期：Complete
• 页码：11-22
• 全文大小：608 K

文摘

A 2t$2t$-cycle system of even order v$v$ is a set ae8d49cb65832f6adb48929b86efe13" title="Click to view the MathML source">C$\mathcal{C}$ of cycles of length 2t$2t$ whose edges partition the edge-set of ca952616aea4104f27" title="Click to view the MathML source">K_v−I$K_v-I$ (i.e., the complete graph minus the ca9e1c4b321dfc5248ad8f8e0fd" title="Click to view the MathML source">1$1$-factor I$I$). If cal-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S019566981630049X-si8.gif">$v\equiv 0(mod2t)$, a set of v/2t$v/2t$ vertex-disjoint cycles of ae8d49cb65832f6adb48929b86efe13" title="Click to view the MathML source">C$\mathcal{C}$ is a parallel class. If ae8d49cb65832f6adb48929b86efe13" title="Click to view the MathML source">C$\mathcal{C}$ has no parallel classes, we call such a system unparalleled.

We show that there exists an unparalleled 2t$2t$-cycle system of order cal-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S019566981630049X-si8.gif">$v\equiv 0(mod2t)$ if and only if aecc1bd" title="Click to view the MathML source">v>2t>2$v>2t>2$.