Hamilton cycles in digraphs of unitary matrices

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• 作者：G. Gutin ; A. Rafiey ; S. Severini ; A. Yeo
• 关键词：Digraph ; Hamilton cycle ; Sufficient conditions ; Conjecture ; Quantum mechanics ; Quantum computing
• 刊名：Discrete Mathematics
• 出版年：2006
• 出版时间：28 December 2006
• 年：2006
• 卷：306
• 期：24
• 页码：3315-3320
• 全文大小：189 K

文摘

A set X8YK-3&_mathId=mml1&_user=10&_cdi=5632&_rdoc=14&_acct=C000050221&_version=1&_userid=10&md5=88456b8bc092f8822015d3895ea2e77e"" title=""Click to view the MathML source"">SV is called a 8d47df6ba398b778de09d"" title=""Click to view the MathML source"">q⁺-set (q^--set, respectively) if S has at least two vertices and, for every uS, there exists vS,v≠u such that 8d05020e93a1dc37f8f"" title=""Click to view the MathML source"">N⁺(u)∩N⁺(v)≠ (N^-(u)∩N^-(v)≠, respectively). A digraph D is called s-quadrangular if, for every q⁺-set S, we have |{N⁺(u)∩N⁺(v):u≠v,u,vS}||S| and, for every q^--set S, we have 8dafbb8796b3a04"" title=""Click to view the MathML source"">|{N^-(u)∩N^-(v):u,vS)}|S|. We conjecture that every strong s-quadrangular digraph has a Hamilton cycle and provide some support for this conjecture.