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

页码：116 / 134

页数：19

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