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

✍ Scribed by Mao-Cheng Cai; Odile Favaron; Hao Li


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

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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.