Colouring the Petals of a Graph
Colouring the Petals of a Graph
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DOI：
10.37236/1699
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发表时间：
2003-01
期刊：
影响因子：
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通讯作者：
David Cariolaro;G. Cariolaro
中科院分区：
文献类型：
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作者：
David Cariolaro;G. Cariolaro
花瓣图是一个连通图 G，其最大度数为 3，最小度数为 2，并且 3 度的顶点集导出一个 2-正则图，而 2 度的顶点集导出一个空图。我们在这里证明，除了从 Petersen 图删除一个顶点得到的图之外，所有花瓣图都是 1 类。这解决了 Hilton 和 Zhu 猜想的一个特殊情况。
A petal graph is a connected graph G with maximum degree three, minimum degree two, and such that the set of vertices of degree three induces a 2‐regular graph and the set of vertices of degree two induces an empty graph. We prove here that, with the single exception of the graph obtained from the Petersen graph by deleting one vertex, all petal graphs are Class 1. This settles a particular case of a conjecture of Hilton and Zhao.