A note on 3-connected cubic planar graphs

被引：4
|
作者：
Lu, Xiaoyun [1 ]
机构：
[1] US Bur Census, Amer Community Survey Off, Suitland, MD USA
来源：
DISCRETE MATHEMATICS | 2010年 / 310卷 / 13-14期
关键词：
Longest cycle; 3-connected cubic planar graph; Hamilton cycle; Hamiltonian; Non-hamiltonian; Tutte fragment;
D O I：
10.1016/j.disc.2010.03.010
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The length of a longest cycle in a graph G is called the circumference of G and is denoted by c(G). Let c(n) = min{c(G) : G is a 3-connected cubic planar graph of order n}. Tait conjectured in 1884 that c(n) = n, and Tutte disproved this in 1946 by showing that c(n) <= n - 1 for n = 46. We prove that the inequality c(n) <= n - root n + 49/4 + 5/2 holds for infinitely many integers n. The exact value of c(n) is unknown. Published by Elsevier B.V.
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页码：2054 / 2058
页数：5
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