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.

引用

页码：171 / 181

页数：11

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