On pancyclic arcs in hypertournaments

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• 作者：Hongwei Li^a ; ^{hwli@sxu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Wenjie Ning^d ; ^{nwj0501@mail.ustc.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Yubao Guo^c ; ^{guo@mathc.rwth-aachen.de" class="auth_mail" title="E-mail the corresponding author} ; Mei Lu^b ; ^{mlu@math.tsinghua.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Hypertournament ; Tournament ; Pancyclicity
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：31 December 2016
• 年：2016
• 卷：215
• 期：Complete
• 页码：164-170
• 全文大小：402 K

文摘

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vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0166218X16303377-si14.gif">mathContainer hidden">mathCode"><math altimg="si14.gif" overflow="scroll">k!kmath>-tuples whose entries belong to mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X16303377&_mathId=si11.gif&_user=111111111&_pii=S0166218X16303377&_rdoc=1&_issn=0166218X&md5=a52f1f460bdad62909fde2c72abda884" title="Click to view the MathML source">SmathContainer hidden">mathCode"><math altimg="si11.gif" overflow="scroll">Smath>. 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Moon (1994) proved that for every strong tournament, there is a Hamiltonian cycle which contains at least three pancyclic arcs. In this paper, we will show that for an arbitrary strong mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X16303377&_mathId=si1.gif&_user=111111111&_pii=S0166218X16303377&_rdoc=1&_issn=0166218X&md5=a545621be75367adeacb1d74e25c6eff" title="Click to view the MathML source">kmathContainer hidden">mathCode"><math altimg="si1.gif" overflow="scroll">kmath>-hypertournament mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X16303377&_mathId=si2.gif&_user=111111111&_pii=S0166218X16303377&_rdoc=1&_issn=0166218X&md5=781edcc1a8af551a049d939234fe3188" title="Click to view the MathML source">HmathContainer hidden">mathCode"><math altimg="si2.gif" overflow="scroll">Hmath> with mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X16303377&_mathId=si3.gif&_user=111111111&_pii=S0166218X16303377&_rdoc=1&_issn=0166218X&md5=2f6d6e3597abd9547d044de6d7ee925f" title="Click to view the MathML source">nmathContainer hidden">mathCode"><math altimg="si3.gif" overflow="scroll">nmath> vertices, where mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X16303377&_mathId=si20.gif&_user=111111111&_pii=S0166218X16303377&_rdoc=1&_issn=0166218X&md5=c927a8ab7d87cc7e804ade881344e588" title="Click to view the MathML source">2≤k≤n−2mathContainer hidden">mathCode"><math altimg="si20.gif" overflow="scroll">2≤k≤n−2math>, there is a Hamiltonian cycle mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X16303377&_mathId=si21.gif&_user=111111111&_pii=S0166218X16303377&_rdoc=1&_issn=0166218X&md5=ebd118223bcc281d04a43cf5f48dfa45" title="Click to view the MathML source">CmathContainer hidden">mathCode"><math altimg="si21.gif" overflow="scroll">Cmath> containing at least three pancyclic arcs, each of which belongs to an mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X16303377&_mathId=si22.gif&_user=111111111&_pii=S0166218X16303377&_rdoc=1&_issn=0166218X&md5=91e6eee7d55a6a769dd34e05e2d19b99" title="Click to view the MathML source">mmathContainer hidden">mathCode"><math altimg="si22.gif" overflow="scroll">mmath>-cycle mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X16303377&_mathId=si23.gif&_user=111111111&_pii=S0166218X16303377&_rdoc=1&_issn=0166218X&md5=85e9743f9e2a3b725ef54247a0f7b563" title="Click to view the MathML source">C_mmathContainer hidden">mathCode"><math altimg="si23.gif" overflow="scroll">Cmmath> for each mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X16303377&_mathId=si24.gif&_user=111111111&_pii=S0166218X16303377&_rdoc=1&_issn=0166218X&md5=8491bdabcee9f8120ce7501dcc326627" title="Click to view the MathML source">m∈{3,4,…,n}mathContainer hidden">mathCode"><math altimg="si24.gif" overflow="scroll">m∈{3,4,…,n}math> such that mathmlsrc">mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0166218X16303377&_mathId=si25.gif&_user=111111111&_pii=S0166218X16303377&_rdoc=1&_issn=0166218X&md5=abeb241e1288204aef660b97a3e4e872" title="Click to view the MathML source">V(C₃)⊂V(C₄)⊂⋯⊂V(C_n)mathContainer hidden">mathCode"><math altimg="si25.gif" overflow="scroll">V(C3)⊂V(C4)⊂⋯⊂V(Cn)math>.