Relative Length of Longest Paths and Cycles in Graphs

被引：0
|
作者：
Huiqing Liu
Mei Lu
Feng Tian
机构：
[1] Hubei University,School of Mathematics and Computer Science
[2] Tsinghua University,Department of Mathematical Sciences
[3] Chinese Academy of Sciences,Institute of Systems Science, Academy of Mathematics and Systems Sciences
来源：
Graphs and Combinatorics | 2007年 / 23卷
关键词：
Relative length; The longest path; Cycle;
D O I：
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学科分类号：
摘要：
For a graph G, let diff(G) = p(G) − c(G), where p(G) and c(G) denote the orders of a longest path and a longest cycle in G, respectively. Let G be a 3-connected graph of order n. In the paper, we give a best-possible lower bound to σ4(G) to assure diff(G) ≤  1. The result settles a conjecture in J. Graph Theory 37 (2001), 137–156.
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页码：433 / 443
页数：10
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