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(3,k)-Factor-Critical Graphs and Toughness

✍ Scribed by Minýong Shi; Xudong Yuan; Mao-cheng Cai; Odile Favaron

Publisher
Springer Japan
Year
1999
Tongue
English
Weight
103 KB
Volume
15
Category
Article
ISSN
0911-0119

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📜 SIMILAR VOLUMES

Equimatchable factor-critical graphs
Equimatchable factor-critical graphs
✍ Odile Favaron 📂 Article 📅 1986 🏛 John Wiley and Sons 🌐 English ⚖ 423 KB

A simple graph G(X, €1 is factor-critical if the induced subgraph (Xx ) admits a perfect matching for every vertex x of G. It is equimatchable if every maximal matching of G is maximum. The equimatchable non-factor-critical graphs have been studied by Lesk, Plummer, and Pulleyblank. In this paper, w

Toughness of graphs and the existence of
Toughness of graphs and the existence of factors
✍ P. Katerinis 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 643 KB

## Theorem 2. Let G be a 2-tough graph. Then for any function f : V(G)+ { 1, 2) such that C xsvCcj f (x) in euen, G has an f-factor. Before stating the second main theorem of this paper it is necessary to make the following definition. Let G be a graph and let g and f be two integer-valued functi

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.