Long cycles in triangle-free graphs with prescribed independence number and connectivity
β Scribed by Hikoe Enomoto; Atsushi Kaneko; Akira Saito; Bing Wei
- Book ID
- 108167356
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 263 KB
- Volume
- 91
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
A cycle C of a graph G is a D~-cycle if every component of G-V(C) has order less than 2. Using the notion of D~-cycles, a number of results are established concerning long cycles in graphs with prescribed toughness and minimum degree. Let G be a t-tough graph on n/> 3 vertices. If 6 > n/(t + 2) + 2-
## Abstract Let __C__ be the class of triangleβfree graphs with maximum degree at most three. A lower bound for the number of edges in a graph of __C__ is derived in terms of the number of vertices and the independence. Several classes of graphs for which this bound is attained are given. As coroll
A simple polynomial-time algorithm is presented which computes independent sets of guaranteed size in connected triangle-free noncubic graphs with maximum degree 3. Let nand m denote the number of vertices and edges, respectively, and let c '= m/n denote the edge density where c < 3/2. The algorithm