Independence Numbers of Planar Contact Graphs
β Scribed by Swanepoel
- Publisher
- Springer
- Year
- 2002
- Tongue
- English
- Weight
- 232 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0179-5376
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
The problem of determining the domination number of a graph is a well known NPhard problem, even when restricted to planar graphs. By adding a further restriction on the diameter of the graph, we prove that planar graphs with diameter two and three have bounded domination numbers. This implies that
For a given planar graph G with a set A of independent vertices, we provide a best-possible upper bound for the minimum cyclomatic number of connected induced subgraphs of G containing A. The extremal graphs are also characterized. @
Let G be a k-connected graph of order n, := (G) the independence number of G, and c(G) the circumference of G. ChvΓ‘tal and Erdo Λs proved that if β€ k then G is hamiltonian. For β₯ k β₯ 2, Fouquet and Jolivet in 1978 made the conjecture that c(G) β₯ k(n+ -k) / . Fournier proved that the conjecture is tr