Set-ordered as a generalization of k-ordered
Set-ordered as a generalization of k-ordered
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集合有序作为 k 有序的推广
DOI：
10.1016/j.disc.2010.05.005
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
K. Ozeki and K. Yoshimoto
中科院分区：
文献类型：
--
作者：
K. Ishii;K. Ozeki and K. Yoshimoto
一个图G称为k-序图，如果对于G的任意k个不同顶点的序列，存在一个以给定的顺序通过这些顶点的圈。一个顶点集S称为G中可圈的，如果存在一个圈通过S的所有顶点。我们将定义“集序”，它是k序和循环性的自然推广。我们还给出了图满足“集序性”的度和条件。这是著名的k-序充分条件的推广。
A graph G is called k-ordered if for any sequence of k distinct vertices of G, there exists a cycle in G through these vertices in the given order. A vertex set S is called cyclable in G if there exists a cycle passing through all vertices of S. We will define “set-orderedness” which is a natural generalization of k-orderedness and cyclability. We also give a degree sum condition for graphs to satisfy “set-orderedness”. This is an extension of well-known sufficient conditions on k-orderedness.