Hamiltonian cycles in hypercubes with faulty edges
Hamiltonian cycles in hypercubes with faulty edges
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DOI：
10.1080/23799927.2018.1538164
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发表时间：
2018-02
影响因子：
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通讯作者：
Janusz Dybizbański;Andrzej Szepietowski
中科院分区：
文献类型：
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作者：
Janusz Dybizbański;Andrzej Szepietowski
摘要Szepietowski [12]观察到，如果超立方体包含一个中途断开的陷阱，那么它就不是Hamilton的。一个真子图T是半不连通的，如果它至少有一半的结点具有奇偶0（或1）。以及连接奇偶校验0（或1，分别）的节点的所有边。在T中，节点在T之外，都是错误的。在本文中，我们描述了所有的陷阱断开一半T的大小，我们考虑的问题，是否存在小集的故障边缘，不基于集断开一半，仍然排除哈密尔顿圈。我们表明，如果与一组故障边缘F包含一个陷阱断开中途T的大小和最小的，那么T是一个路径或哈密尔顿。我们还描述了启发式识别nonhamilton立方体，也不包含中途断开的陷阱。
ABSTRACT Szepietowski [12] observed that the hypercube is not Hamiltonian if it contains a trap disconnected halfway. A proper subgraph T is disconnected halfway if at least half of its nodes have parity 0 (or 1, resp.) and all edges joining the nodes of parity 0 (or 1, resp.) in T with nodes outside T, are faulty. In this paper, we describe all traps disconnected halfway T with the size and we consider the problem whether there exist small sets of faulty edges that are not based on sets disconnected halfway and still preclude Hamiltonian cycles. We show that if with the set of faulty edges F contains a trap disconnected halfway T that is of size and is minimal, then T is a path or is Hamiltonian. We also describe heuristic that recognizes nonhamiltonian cubes, also these ones that do not contain traps disconnected halfway.