𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Codiameters of 3-connected 3-domination critical graphs

✍ Scribed by Yaojun Chen; Feng Tian; Bing Wei

Publisher
John Wiley and Sons
Year
2001
Tongue
English
Weight
110 KB
Volume
39
Category
Article
ISSN
0364-9024

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

A graph G is 3‐domination critical if its domination number γ is 3 and the addition of any edge decreases γ by 1. Let G be a 3‐connected 3‐domination critical graph of order n. In this paper, we show that there is a path of length at least n−2 between any two distinct vertices in G and the lower bound is sharp. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 76–85, 2002

📜 SIMILAR VOLUMES

Independence and hamiltonicity in 3-domi
Independence and hamiltonicity in 3-domination-critical graphs
✍ Favaron, Odile; Tian, Feng; Zhang, Lei 📂 Article 📅 1997 🏛 John Wiley and Sons 🌐 English ⚖ 144 KB 👁 3 views

Let δ, γ, i and α be respectively the minimum degree, the domination number, the independent domination number and the independence number of a graph G. The graph G is 3-γ-critical if γ = 3 and the addition of any edge decreases γ by 1. It was conjectured that any connected 3-γ-critical graph satisf

Critical graphs for subpancyclicity of 3
Critical graphs for subpancyclicity of 3-connected claw-free graphs
✍ Ronald J. Gould; Tomasz Łuczak; Florian Pfender 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 173 KB

## Abstract Let ${\cal{F}}\_{k}$ be the family of graphs __G__ such that all sufficiently large __k__ ‐connected claw‐free graphs which contain no induced copies of __G__ are subpancyclic. We show that for every __k__≥3 the family ${\cal{F}}\_{1}k$ is infinite and make the first step toward the c

Some 3-connected 4-edge-critical non-Ham
Some 3-connected 4-edge-critical non-Hamiltonian graphs
✍ Yang Yuansheng; Zhao Chengye; Lin Xiaohui; Jiang Yongsong; Hao Xin 📂 Article 📅 2005 🏛 John Wiley and Sons 🌐 English ⚖ 79 KB 👁 1 views

## Abstract Let γ(__G__) be the domination number of graph __G__, thus a graph __G__ is __k__‐edge‐critical if γ (__G__) = k, and for every nonadjacent pair of vertices __u__ and υ, γ(__G__ + __u__υ) = k−1. In Chapter 16 of the book “Domination in Graphs—Advanced Topics,” D. Sumner cites a conjectu

Cyclability of 3-connected graphs
Cyclability of 3-connected graphs
✍ Amel Harkat-Benhamdine; Hao Li; Feng Tian 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 151 KB 👁 1 views
Hamiltonian properties of domination-cri
Hamiltonian properties of domination-critical graphs
✍ Ewa Wojcicka 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 445 KB

## Abstract In this paper we show that every connected, 3‐γ‐critical graph on more than 6 vertices has a Hamiltonian path.

The k-Critical 2k-Connected Graphs for k
The k-Critical 2k-Connected Graphs for k∈{3, 4}
✍ Matthias Kriesell 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 180 KB

A noncomplete graph G is called an (n, k)-graph if it is n-connected and G&X is not (n&|X | +1)-connected for any X V(G) with |X | k. Mader conjectured that for k 3 the graph K 2k+2 -(1-factor) is the unique (2k, k)-graph. We settle this conjecture for k 4.