Detour-saturated graphs

被引：5
|
作者：
Beineke, LW [1 ]
Dunbar, JE
Frick, M
机构：
[1] Indiana Univ Purdue Univ, Ft Wayne, IN 46805 USA
[2] Converse Coll, Spartanburg, SC 29302 USA
[3] Univ S Africa, Unisa, South Africa
来源：
JOURNAL OF GRAPH THEORY | 2005年 / 49卷 / 02期
关键词：
longest path; detour; detour-saturated; unicyclic;
D O I：
10.1002/jgt.20069
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A graph is said to be detour-saturated if the addition of any edge results in an increased greatest path length. In this paper, we add to the relatively small amount that is known about detour-saturated graphs. Our main result is a determination of all connected detour-saturated graphs with exactly one cycle. (The family of detour-saturated trees was found by Kaszonyi and Tuza [7].) We also show that the smallest detour-saturated graph of girth 5 is the graph obtainable from the Petersen graph by splitting one of its vertices into three, each of degree 1. (c) 2005 Wiley Periodicals, Inc.
引用
收藏
页码：116 / 134
页数：19
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