ON THE HAMILTONIAN NUMBER OF A PLANE GRAPH

被引：1
|
作者：
Lewis, Thomas M. [1 ]
机构：
[1] Furman Univ, Dept Math, Greenville, SC 29613 USA
来源：
DISCUSSIONES MATHEMATICAE GRAPH THEORY | 2019年 / 39卷 / 01期
关键词：
Hamiltonian cycle; Hamiltonian walk; Hamiltonian number; Hamiltonian spectrum; Grinberg's theorem; planar graph; SPECTRA; WALK;
D O I：
10.7151/dmgt.2084
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The Hamiltonian number of a connected graph is the minimum of the lengths of the closed spanning walks in the graph. In 1968, Grinberg published a necessary condition for the existence of a Hamiltonian cycle in a plane graph, formulated in terms of the degrees of its faces. We show how Grinberg's theorem can be adapted to provide a lower bound on the Hamiltonian number of a plane graph.
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页码：171 / 181
页数：11
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